In theory, somewhat easy? The strategy does present a number of complications, however, and while I don't have any sources attesting to this being "a thing" during the American Civil War (which is what I assume OP is talking about), we do know something about battlefield deserters and wounded, which can help inform part of the answer to this question.

Really, though, it all depends on the battle. American Civil War battles varied in terrain, the number of combatants engaged, duration, intensity of fire/artillery, not to mention the ebb and flow of the specific conflagration itself. Take, for example, the second day of the battle of Gettysburg. If you were a Confederate soldier that employed this tactic during the assault on Little Roundtop, if you waited until after that specific part of the battle was over, you'd find yourself behind enemy lines and in Federal custody as a POW. Odds-wise, you were about as likely to die from illness as a POW as you were a soldier in battle, so that doesn't offer much of a benefit in the long-term. The same would go for a Confederate during the 3rd day during Pickett's Charge: playing dead didn't necessarily increase your odds of survival if captured.

Let's say it is an even more nebulous battle, like Chickamauga or Shiloh, where the lines wavered back and forth quite a bit, and there weren't as many fortified positions (at least for very long). On either side of that battle, the lines and breakthroughs changed very fast, so playing dead once again didn't necessarily help a person if they just wanted to lay down, stay behind, and wait for things to shake out. It might take days for you to get up, unnoticed, and wander off or back to your unit, during which time a battle might have raged on top of you several times.

But let's say you were able to play dead behind your own army's lines, ending up in your side's echelon. In a battle like Fredericksburg, if you were a Confederate, you might be able to lay down behind the stone wall on Marye's Heights, or in the woods where Jackson held the right wing, and wait it out, sure. But then you'd have to explain why you were not with your unit during roll call following the battle, and without a wound to explain yourself. Deserters were regularly shot, and to quit fighting in the middle of a battle, even if you didn't run, would put you in a very tough spot needing a lot of explanation.

This is all aside from the fact that a hot, active battlefield during the Civil War was about the last place on the planet where you'd want to be during a nap. Stray bullets, artillery shells, and even the trampling feet of a couple hundred fully armed men raining down on top of you would not present a very inviting picture. Being in the thick of one of these battles was unpleasant by all accounts, and harrowing to say the least, but plopping yourself down in the middle of it all, and just hoping that a stray bullet, shell, or enemy unit didn't find you was more risky than just rolling the dice, staying with your unit, and trusting in their collective fate. I don't have any sources handy that address this specifically, but I suspect it is because it wasn't a regular occurrence (for many of the reasons outlined here).