Are there any accounts of this? Pretending to be dead and then running away after the rest of the armies cleared, it sounds like a good deserting strategy.
I can think of two examples of soldiers playing dead - Lyudmila Pavlichenko and John Steele.
Lyudmila Pavlichenko was a Soviet sniper during WW2. One day she was up in a tree scouting the area when a German sniper spotted her. He kept firing at her and there wasn't much she could do in a tree so she pretended she was hit and let herself fall out of the tree. She laid on the ground for hours pretending to be dead until it was finally nighttime and she got up and left.
John Steele was a paratrooper during WW2. On D-Day, his parachute got caught on a church tower and so he played dead for a couple hours before the Germans realized he was alive and took him prisoner.
I hope this answers your question a little bit. It doesn't answer how often something like this would happen but I think it's safe to assume that since there are two true stories of a soldier playing dead that it most likely happened a few other times too.