Not entirely. In the early days of westward expansion, we can probably assume that people would have preferred to settle in the Midwest where there were nice flat plains and rich soils suitable for farms, rather than the steep, rocky hills of Appalachia. However, people were blocked from moving further west not just by the physical barrier imposed by the rugged mountains, but by conflict with Native American groups and the various treaties established to try to mitigate the violence. As far as I'm aware, there is no evidence that people loaded up their wagons intending to go to to Illinois or whatever, had a rough time once they hit the mountains, and figured, "welp, I'll just build my cabin here now." The mountains of eastern Kentucky and West Virginia were settled intentionally by people who really wanted space to build farms and such, but were constrained by the fact that much of the land in the East had been already been claimed, and the fact that settling further west would have invited conflict with Native Americans.

The Appalachian Mountains were first settled by people of European origin beginning in the 18th century. (Before that, there had been hunters and trappers and such, but not really people with families.) However, there were already people living there--Native American peoples including the Cherokee and Shawnee. Unsurprisingly, these indigenous peoples were pretty pissed about all the white folks who were taking over their land, and violent conflicts between Native Americans and white settlers were incredibly common. A series of treaties attempted to establish boundaries for westward expansion--for example, the Treaty of Albany in 1722 which said that people of European origin were allowed to settle anywhere east of the Blue Ridge.

Over time, individual settlers would risk violent encounters and settle west of the official boundary line. Some of these settlers were encouraged by land speculators and boosters who aggressively promoted settlement of the backcountry, others were simply looking for inexpensive farmland after all the good land further east was already claimed. This ultimately prompted several "Indian" wars in the backcountry and the creation of new treaties which were in turn ignored.

Good farmland in central Appalachia is relatively scarce, because the topography is so hilly and the soil is fairly thin and rocky. People developed a variety of techniques in order to make it possible to farm in the hills. For example, swidden agriculture ("slash and burn") was one solution to poor-quality soil--people used fires to quickly clear heavily-forested hillsides and add nutrients to the soil. Settlers from places like Ulster Ireland and Scotland also brought with them agricultural strategies for dealing with poor soils, including crops like turnips, barley, and rye, as well as patterns of livestock grazing. (And, of course, a tradition of preserving crops by distilling them into whiskey, which developed into the tradition of making moonshine!) German and Scandinavian settlers brought with them forestry-management practices and were the first to build the log cabins that have become a part of Appalachian backcountry vernacular architecture.

Interestingly, many of the early settlers of central Appalachia didn't actually own the land they settled on--many were leasing land or even squatting on land owned by large land speculators. This pattern can be seen today in the fact that large portions of Appalachia are owned by absentee landowners who funnel away value from timber, coal, or other activities away from Appalachian communities.

Note: I'm not a historian, but I am an anthropologist who works in Appalachia

Sources:

Williams, John Alexander. 2002. Appalachia, A History. Chapel Hill: University of North Carolina Press.

Davis, Donald Edward. 2005. Where There Are Mountains: An Environmental History of the Southern Appalachians. Athens: University of Georgia Press

Edit: formatting

I think the earlier answer misses a big chunk of the crucial history that involves the British and the French in colonial North America. In fact, the North American theater of the Seven Years War, the "French and Indian War", was largely caused by the colonial land boundary west of Appalachia.

The border between New France and British North America was in dispute until the 1750s, but with neither side doing much about it. In 1749, Great Britain approved the formation of the Ohio Company of Virginia, a real estate venture funded mostly by rich Virginians back east that would survey land in "Ohio Country" (i.e. the land just west of the Appalachian Mountains) and start putting it up for sale to British colonists.

The Ohio Company began blazing suitable roads past the Appalachians, but quickly ran into a big problem. The French were claiming the land by manning newly built military forts in the area. Fort Machault, Fort Le Boeuf, and Fort Presque Isle were a line of French forts built between what's now Erie, Pennsylvania, and an area north of Pittsburgh, to defend their North American land claim.

This threatened the investment of the investors in the Ohio Company, who had sunk a bunch of money into the land beyond the Appalachians. One such person who stood to lose a lot of dough was the colonial governor of Virginia, Robert Dinwiddie. To defend Britain's land claim (and his own investment), he sent troops from the Virginia Regiment to go tell the French to leave, under the leadership of a young major named George Washington.

He went, the French refused, and Washington went back to Williamsburg to tell Dinwiddie. Dinwiddie then appointed a representative of the Ohio Company, William Trent, as a Captain in the Virginia Regiment and sent him out to what is now downtown Pittsburgh, Pennsylvania, to build a fort in defiance of the French.

Trent had less than a hundred men, and soon after their arrival, 800 French troops met them there, and Trent and his men agreed to leave. The French then built Fort Duquesne on the site.

In March 1754, Dinwiddie promoted George Washington to colonel, and sent him back out there, this time building a fort a few dozen miles south of Fort Duquesne. The French yet again issued a summons for Washington and his men to leave the area. But during the night, Washington recruited some local reinforcements and some Indian allies, and they ambushed the contingent of French soldiers who had delivered the message. The Battle of Jumonville Glen became the opening battle of the French and Indian War. With the French and British not at war at that time, it was also a contributing cause to the larger Seven Years War between the two European nations back in Europe.

The French soon arrived with more troops, and heavily outnumbered, Washington and his men were forced to surrender at the Battle of Fort Necessity on July 3, 1754.

The following year, General Edward Braddock led 2000 soldiers out to Fort Duquesne to capture the fort and control of the Ohio Country, but Braddock's Expedition was defeated and Braddock was killed.

The French continued to control Fort Duquesne until 1758, when Forbes' Expedition led 6000+ troops to go capture Fort Duquesne, and were successful after winning the Battle of Fort Duquesne on September 14, 1758.

The British built Fort Pitt on the site, and France recognized Britain's control of Ohio with the treaty that ended the Seven Years War in February 1763. The Treaty of Paris gave all French land east of the Mississippi River to Great Britain.

But several of France's Indian allies in the area weren't willing to give up so easily. The end of the French and Indian War was the start of Pontiac's War. The Siege of Fort Pitt led to the Battle of Bushy Run in the summer of 1763, and while Pontiac and his allies were unable to force the British to vacate the area, the British did agree not to settle the area any further. King George III's Royal Proclamation of 1763, issued in October, ordered no settlement in North America west of the Appalachian mountains.

This proclamation has often been cited as one of the early contributing factors to the American Revolution. The Ohio Company had continued to operate throughout these years and its investors still wanted to see a return on the land they had purchased. They had been unable to attract few actual settlers, with the land being in dispute by two European powers and several local Indian tribes.

Another Indian treaty in 1768, the Treaty of Fort Stanwix, moved the line where British could settle a bit further west, but no real settlement had begun when the American Revolution put on hold any further plans.

The British gave the area to the United States at the Treaty of Paris in 1783 that ended the Revolution, and then the U.S. government negotiated settlement rights with area Indian tribes with the Treaty of Fort McIntosh in 1785. Congress subsequently established the Northwest Territory with the Northwest Ordinance of 1787, which opened up the area past the Appalachians for settlement. Further treaties and ordinances pushed settlement further and further west.

It should be said that typically, as a settler, you would have made some kind of monetary arrangements for a land purchase before you left for your destination. You wouldn't necessarily have picked out a particular lot, but in most cases, you would have at least talked to some kind of real estate agent, i.e. a representative of the Ohio Company or some other such company, and made some kind of down payment or deposit on a piece of land in a surveyed area that the company was specifically selling/leasing. Once you got there, you would then be able to pick out a particular lot, or among some subset of lots the company was currently offering for sale/lease. So, to just stop halfway to your intended destination would mean you were giving up the down payment you had already made, or the deposit on the lease you had signed, unless by chance the place you stopped in instead also had land for sale/lease by the same real estate entity and you could make arrangements to change the terms of your contract.

There were squatters and such, but most often, squatters weren't motivated in going it alone in some wilderness. They were typically going to an area of unsurveyed land near some already surveyed land that was already being settled, to force the government or local real estate concern to sell the land to you when it wasn't yet for sale. Different people were motivated by different factors, but in any case, most squatters weren't far from where genuinely purchased land was already being settled.

TL;DR: No, there is no historical truth to people stopping in Appalachia that were on their way elsewhere. Before the 1740s, the European powers hadn't yet tried to expand permanent settlement past the Appalachian mountains. And then when they did, control of the area became disputed between the British and the French in the 1750s, and then between the British and the Indians in the 1760s, and then fighting between the British and the Americans further delayed in settlement in the 1770s and 80s.

It wasn't until the Northwest Ordinance of 1787 that the U.S. government was in a position to finally open the area for purchase and settlement.

So before that, you really couldn't go much past the Appalachian Mountains as a prospective British settler. And then after that, you could, and you did, since much of the most hospitable land for farming in the Appalachian mountains had already been claimed or otherwise wasn't yet up for purchase.

Sources:

The Ohio Company: Its Inner Workings by Alfred Proctor James

Braddock's Road by Henry Temple

A Mighty Empire: The Origins of the American Revolution by Marc Egnal

History of Pittsburgh and Environs by George Thornton Fleming

Along the Ohio Trail: A Short History of Ohio Lands by Tanya West Dean and W. David Speas

Further Reading:

Early Western Travels, 1748-1846: A Series of Annotated Reprints... ed. by Reuben Gold Thwaites