Yes, plenty.

I recommend reading "British Soldiers, American War" by Don Hagist. It's a collection of first-hand accounts of British soldiers who fought in the Revolution - several of whom deserted and lived out the rest of their lives in America.

One such soldier highlighted in the book is John Robert Shaw, a member of the 33rd Regiment who was captured by the Americans shortly before the battle of Guilford Courthouse, and sent to a prison camp in Lancaster Pennsylvania. He remained there for a few months before eventually escaping. Afterwards, he roamed the countryside for a while, doing a series of odd jobs here and there before eventually joining the rebel cause - presumably out of fear that the if he didn't, someone would hand him back over to the British for reward money. The war ended soon after, and he eventually settled in Kentucky, where he lived out the rest of his life as a well digger. He died in 1813 in a work-related accident.

Another example provided is William Crawford of the 20th Regiment, who, like Shaw, had a brief stint in prison. During his captivity, he fell in love the daughter of the sheriff, and absconded with her. Unfortunately, their relationship quickly became dysfunctional. He developed a drinking problem, which led him to kill one of his sons in a fit of rage - for which he was hanged in 1823.

There are others, as well, who aren't mentioned in the book, like Thomas Sullivan of the 49th Regiment, who, upon arriving in America, found that the Americans were "striving to throw off the yoke," which induced upon him "a serious consideration to share the same freedom which America strove for." After deserting, he moved with his wife to Philadelphia, where "upwards of eight hundred deserters" arrived before him.