No, Sherman's men did not eat as well as they could have if they'd not cut their 'ties' to their own supplies. There was very little food. Even the guards at Andersonville were hungry. It was found after the war that there was a very real effort to keep supplies mandated for prisoners at Elmira, Camp Chase and other prisons from reaching the prisoners.
That wasn't the problem with Southern prisons. To help relieve the situation, there was an effort to return some of those at Andersonville and it was refused.

Pam