Sounds like a wonderful idea...animals can provide a means of getting out of depression and this could help alleviate overfilled shelter issues. My only concern is, what if a solider lashes out? How great is the risk of harm to the animal?
I suspect that like any program of this nature, there's a screening process. That said, I'm not sure there's a way to remove any and all risk...no more so than there would be in someone not suffering the effects that these guys are.