Absolutely. Conditions within the British Army, especially in the colonies, weren't very good. Many men were pressed in to service and most private men were poor and treated poorly. I've been able to find individual cases in books that men deserted to fight for the Americans willingly.

One large case of  desertion was Burgoyne's Convention Army after the Battle of Saratoga in which about 900 men "deserted" but were actually prisoners of war who either switched sides or were released in to the land with a promise never to fight again. Here's a great resource on British desertion/defection during the Revolution and it discussed the Burgoyne Army:

http://books.google.com/books?id=xSprXYNmduwC&lpg=PA73&dq=british%20soldiers%20switched%20sides%20revolutionary%20war&pg=PA73#v=onepage&q=british%20soldiers%20switched%20sides%20revolutionary%20war&f=false

Edit: I'm mobile and I don't know if the above link is working. If not, type in the Search Bar to search in the book "desert" and the instance I was referencing is on page 73.