Not happening, Old Wustorians have noticed that in every interview he does for TV they only give him already prepared questions were he begin his tale about how he, Frank and the dogs were almost raped by Gamergate operatives, there is no way in the universe that he accept to go in a debate against a politician with actual years of experience, heck if he manage to piss off enough people maybe the media would do the job for Lynch
unless Frank is coaching the interviewer or he is in a controlled environment he is not going to even think in debating, he runs at the first sight of a problem, Lynch in other hand has experience dealing with assholes that even digged his past to get dirt on him, but he was composed, played the game like the pros and won, meanwhile John gets triggered every time people deadname him on twitter (well in the past, apparently he has learn to use filters to mute his deadname, after all his buddies on twitter were fired)
But like you say if in a high doses of nyquill he decide to debate he is going to be raped so hard because all of John themes are the same shit "Muh infosec, muh womens, muh engineering", and people that vote dont give a shit about it
If by ideology you mean believing he is going to be crowned as the queen of feminism then yes