No, that's not at all the case. There was no "gun control" as we'd think of it at the time, although the immediate cause that precipitated the fighting at Lexington and Concord in 1775 -- which most people think of as the start of the Revolutionary War -- was an effort by the British general in charge of the American colonies to seize a collective store of powder and arms kept by and for the Massachusetts colonists. (The general's opinion was that the collective store was eventually royal property, and the colonists' that it was collective property meant for the defense of the colonies, against attacks from any quarter.)

I wrote a long answer to what precipitated the fighting at Lexington, but OP deleted the question, so I'll reproduce it below this comment. It goes into not just the fighting on April 19, 1775, but also the background to the conflict in the colonies.

Hard to add much to jschooltiger, here, but up until the Revolution, the colonists had been given the job of defending themselves. There were even militia laws that required men to own a firearm. Overmuch has been made of these militia laws, and it seems that they were often pretty badly enforced: hurriedly revived when there was a threat from Spain or France, then somewhat ignored again. But still, there were only militias, there was no standing army.

When the colonies ignited the Seven Years War and found themselves facing the French and the Native Nations, their disunity and their various militias turned out to be inadequate to the task, and eventually England sent regular troops. Once the Seven Years War was concluded the cost of this, and the maintaining of those troops when they were left in garrison, were some of the larger grievances that started the revolt. The colonists still felt as though they alone should be in charge of their defense. The famous Powder Alarm, that jschooltiger refers to, is a great example of this- the Boston residents felt the gunpowder was to be for their own use ( and had already withdrawn some of it) , the Governor felt it was for the use of the King's soldiers. Technically, the Governor was correct- but the colonists had had more than a hundred years of local militia-based defense and thought otherwise.

Also, some people ( like gun rights advocates) today conveniently place the Powder Alarm before the troubles in order to make it a cause. But when the Powder Alarm happened, Boston Bay was already on the edge of revolution. The Powder Alarm was a symptom of that, not a cause.

Robert Richmond: Powder Alarm 1774

M.L.Brown : Firearms in Colonial America