I can speak with the most comfort on battles from the American Revolution, and I can say that yes, they did, and mostly for the same reasons: desertion, or being overrun in battle.

There has been a lot of recent scholarship about how granular and devolved in nature many battles during the American War of Independence were. While the myth that the Patriots won the war by hiding behind rocks and trees is certainly false, many battles occurred in wooded or broken terrain. This meant that regiments/battalions, the basic fighting unit of the day, had a very difficult time keeping central operational command during a battle. At places like White Plains, Oriskany, or Guilford Courthouse, the lines of battle zigged, zagged, and overlapped, rather than keeping perfect order at a hundred yards distant. In this kind of fighting, small groups of men could become isolated, and thus easily surrounded and captured.

Desertion to the enemy was a form of surrender, and one that both sides in the Revolution profited from. Here, surrender by lone individuals or very small groups was most common - I can't think of any units that switched sides as a block, though the total number of deserters who took up arms must have numbered in the thousands.

The best-known new histories of battle during the American Revolution are:

Lawrence Babbits, A Devil of a Whipping: The Battle of Cowpens

Lawrence Babbits and Joshua B. Howard, Long, Obstinate, and Bloody: The Battle of Guilford Courthouse (much of my response is informed by this book in particular)

Matthew Spring, With Zeal and with Bayonets Only:The British Army on Campaign in North America, 1775–1783