Yep, from what I've read of Liesl, they wouldn't have gotten along at all. My idea, actually, was that he either joined and left pretty quickly (not respecting her approach, since they differ so much), or didn't join for the same reason, but saw his opportunity now that she's left. But I actually think having her kick him out would work even better, since it would give him more motivation to usurp her aims after she's left. He has, after all, just randomly seized power ("just named himself" the new leader, basically) a term into the year, so hardly the poster child for cooperation (on the other hand, his NPC sister might have a lot more in common with Liesl, I think).
Because he is an idiot, let's be real. He's awful. They should hate him. I hate him. I'm under no illusions as to how ridiculous he is as a character and a person. The main aim in making him was to elicit conflict with other students (and authority figures), so that's also great. His delusion and self-importance (as well his misguided aims and beliefs) mean it's pretty much inevitable.
As for Destrey and Selwyn, that's perfect! Honestly I'd love to get him in trouble as often as possible. It would frustrate him and just make him act out more, culminating in an annoying game of cat-and-mouse. Would probably teach him to be more subtle, too.
If you'd like to thread any of your lot, students or professors, with him and air the dislike or disapproval I'm up for that! We could easily find a variety of excuses for any sort of conflict or punishment to occur.