Yes an incel chad is a contradiction. But many people like on IT or AHS think "incel" is just an ideology, not something that you are.

So the idea would to make a chad who identifies as an "incel". This chad would dish out blackpills and would try to get matches to agree with his views.

It should be more than doable, we have had racist chads, sexist chads, nazi chads, and felon chads all with major success. Incel chad would really get to deniers of the blackpill.