General Grant would have no problem with Gen. Hood leading one of his corps had Hood been a union officer. They were simpatico.
Nor did Lee. He was a brigade then division commander in the ANV.
Possibly. Hood as a brigade commander led the Texas Brigade when it broke the Union line at Gaines Mill. As a division commander he almost shattered the Union left at Second Bull Run and turned back the Union attack on the Confederate left flank at Antietam. While not agreeing with the attack on the second day at Gettysburg - Longstreet wasn't thrilled with it either - he led his men and almost broke the Union line once again. His corps almost won the day at Chickamauga. So yeah, I think Grant would have been thrilled to have Hood as a division or corps commander. Yes, both were simpatico in that both wanted to win. But as an Army commander Grant was heads and shoulders above Hood, as well as his peers.