I say it would depend on the actual charge. For a major Union general to be prosecuted by his own government for a war crime would require some sort of gross violation of policy. It would require an act that shocked the Union population, majority of other federal officers, and a good chunk of government officials. Even then, Sherman may have been simply relieved of command as punishment.

It is entirely possible for soldiers and officers to be punished for war crimes. We may find examples in just about every war where individuals were arrested and sometimes executed for murder, torture, etc. But, again, these usually arise when the act shocks the other soldiers and officers to the point of taking disciplinary action.