It would have made no difference whatsoever.
T'Kuvma was an extremist who wanted war, Starfleet couldn't have won, the outcome was a foregone conclusion, and the real story is where Starfleet goes from here.
They don't think that I don't think - they have just charged her with a couple of very serious crimes that still carry the death penalty in some militaries:
- Assaulting a superior officer.
- Mutiny.
Her only blame could be from killing T'Kuvma instead of capturing him, but there were no witnesses, and I doubt it would have made much difference. Take the opinion of civilian prisoners with a grain of salt - just being there and accidentally killing the Klingon is enough for someone not privy to the full picture to say Starfleet started it.