Would Stannis have executed.....(Spoilers Extended)

Tyrion if he won the Blackwater and had him captive? Stannis acknowledges that good men fight for the wrong side, either because they are misinformed, or supporting their liege lord. If Tyrion lied and said he knew nothing of the twincest, and was fighting for his family and the boy he believed to be Robert's true heir. Stannis himself has faced a similar dilemma in Robert's Rebellion.

Stannis pardoned Renly's lords. Admittedly that may be more for practical reasons than anything else, but they were absolutely traitors in his eyes, with no excuse for their treason. Tyrion has a much better argument that he did no intentional treason towards Stannis.

Would Stannis really kill this valuable hostage, who has a perfectly justified case for all the things he did? Tyrion would of course also deny anything to do with the attempts on Bran's life. Tyrion also might earn some respect for leading a sortie, as a dwarf, while outnumbered and in a losing fight.