Possibly, it's hard to say. I would wager that it is possible given that they are still human. They are probably highly resistant towards PTSD though since they have been indoctrinated from birth towards the very purpose of war. Coupling that with their average survival rate and I think that most would not live long enough to ever experience it.
Most soldiers only get PTSD when they have returned from war, but clones even if they win and survive a battle it would be straight on to the next one until the day they died, which would also be relatively quick since they age way faster.
There is also the issue with the mind control chips that makes them do whatever they are ordered. Most clones had quite a bond with their Jedi commanders (see Star Wars: The Clone Wars, Plo Koon had quite the bond) yet the clones did not hesitate for a second to shoot them all down.
I can't conclude for certain, though I would lean towards a yes.
Now these guys I would go for a definitive yes. In the game Star Wars: Republic Commando you can already hear the major amount of stress the clones have when they leave behind their brother. These clones also displayed a vastly different character and expressed themselves more as individuals compared to their normal brethren.
I also do believe there is a comic of commando clones where one gets traumatized but I am not 100% sure on that one.
Most of my answer is speculation based on given facts and displays so feel free to correct me and improve my answer with canon sources and quotes. (I'm not even certain republic commando is canon anymore.)
I'm all up for a debate :)
Edit: as Thunderforge stated, Star Wars: Republic Commando is now part of the legends continuity.