As far as I'm aware, most historians consider McWhiney to be at best severely misguided (and at worst, a Confederate-apologist hack). There is a connection between the Jacobites and the Confederacy, but it is based on popular literature rather than actual history.

The majority of whites in the south in the mid-19th century were of either English or Scots-Irish origin. The tidewater planter families (such as that of Robert E. Lee) were primarily descended from wealthy families from the south of England. Most of these were supporters of the Royalist, or "Cavalier," side in the English Civil War. The Scots-Irish were descendants of lowland (i.e. Presbyterian and non-Gaelic-speaking) Scots who moved to Ulster in Ireland in the 17th century, and from there moved on to North America, where they settled mainly in the Appalachian mountains. Both the tidewater planters and the Scots-Irish typically supported the patriot side in the American Revolution. (For more about this I'd recommend David Hackett Fischer's book Albion's Seed. IMO his thesis is a bit too "tidy" but all the same it's a great introduction to the main British regional cultures that combined, with others, to form American culture.)

There was a community of Highland Scots in North Carolina, who maintained their Gaelic language and cultural traditions until around the time of the Civil War. In the pre-Revolutionary days it was centered on two towns called Cross Creek and Campbeltown (which are now known by the name of Fayetteville). At the time of the Revolution, very few of these Highlanders supported the rebel side, with most fighting for the loyalists or attempting to remain neutral and hoping the conflict would blow over. (Side note: The reason for this support of the British empire after the Jacobite rebellions has aroused some confusion. If you have any questions about that I'd be happy to answer.) As such, the Highlanders (and Scots in general) gained a very negative reputation throughout the fledgling United States. Many of them wound up leaving for Nova Scotia or even going back to Scotland. The descendants of those who stayed did in many cases end up fighting for the Confederacy in the Civil War but were definitely a small minority.

How did the reputation of the Highlanders, both in Britain and North America, get turned around into the romantic image we are used to? It was basically down to one man--Sir Walter Scott. While Scott's novels have largely fallen out of favor today (and he himself seems to have recognized that he was a better folklorist than he was a writer), they were absolutely massive in the early to mid-nineteenth century. They promoted an image of the Highlander as being gallant, romantic, honorable, and courteous, and kicked off a bout of Highland-mania that spread throughout the English-speaking world and elsewhere. The notion of clan tartans, essentially an invention by Scott, still survives today, and many believe that this was an ancient historical practice when it was nothing of the sort. Due to Scott, Scotland's identity began to be increasingly wrapped up in Highlandism (a romanticized image of the 18th-century Highlands) and "tartanry." And it survives today--after the success of Outlander (which, to its credit, does attempt to deal with real history, though it still gets caught up in a bit of over-romanticism IMO), there is now a whole subgenre of "Highlander Romance" novels!

Anyway, to return to the topic at hand, many of those who led the Confederate movement, who were mainly of English origin, saw themselves in Scott's Highlanders--the emphasis on gallantry and nobility in particular. As many of Scott's books focused on the Jacobite rebellion, the Confederates began to increasingly relate to the Highland Jacobites' struggles against the Hanoverian government, equating it to their own situation. As such, the Confederate mythology and self-image arguably has two main origins--the Cavaliers of the English Civil War and Scott's romanticized Jacobites. However, any attempt to link the Confederacy to the real Jacobites usually fails, because there really isn't a connection. Most American colonists, including those in the South, celebrated the defeat of the Jacobites at Culloden, and Highland immigration to the southern US was far too minor to have had any major impact.