I think its nonsense to say that Hitler failing to kill himself is inherently ASB, the world is full of people who have failed to kill themselves, all that needs to happen is for him to be incapacitated, betrayed, or taken by surprise.
If captured alive, the security surrounding Hitler would have been pretty substantial, so he may well be deprived of the chance to kill himself while in custody. Assuming this to be the case he would no doubt stand trial at Nuremberg, the suggestion that Stalin would have put some sadistic desire to keep Hitler in a private dungeon above the political and public importance of a international trial misjudges the man.
Which takes us to the root of the question, how would the trial of Adolf Hitler go? How would he behave on the stand? I think the answer to that is probably some varying degree of non-cooperation. This isn't like after the beer hall putsch, Hitler has nothing to gain by extravagnt rhetoric, broken and defeated, humilliated, mentally unstable, betrayed by everyone and disillusioned with the German people themselves he will be unrepentant, depressed, angry, and likely just want the whole thing over so he can go to his inevitable death.
So I think he's either going to just sit there and completely refuse to acknowledge the court, or he may take the opportunity to launch one final tirade against, well, pretty much everyone in the world at this point. Then he dies.
As for the affect on neo-nazis and people who glorify Hitler, I'm inclined to think that no matter how incoherent he is on the stand they'll be able to look past it so shouldn't damage his standing too much. You'd probably find modern neo-nazis raging against the injustice of his trial, and if he managed to say anything halfway memorable during his defense such a phrase would be seized on by neo-nazis and repeated ad nauseum as the fuhrer's glorious final words.
As much as I hate Hitler I kind of wish he could have lived long enough to answer many questions about the Nazis and how Germany conducted the war. He could share many secrets about negotiations, reasons for different actions, and insights into the people around him.
I know it sounds crazy but we can learn alot from studying such a man.
Hitler would have zero interest in explaining anything to anyone, so the only way you're going to get any kind of information would be torture following his capture, which does not always give the best insights.