If they have standing it would proceed at least in regard to standing.
You do understand the legal concept of standing?
From the lay legal, Standing is demonstrated by the person bringing the suit having been harmed and being able to show that harm. The key to “standing”, to which it is unlikely anyone will have such standing is because although they may be able to say they may be harmed in the future, standing is for harm already done. Our civil legal system is designed to redress persons harmed (past tense), not as a preventative for a hypothetical future harm.
The only stop-gap is when Congress certifies the results of the Electoral College, after the election. My understanding is that it requires more than one Representative to object to certification “for cause”.
Once a President is sworn in he is President regardless of how he gets there.
Are you saying that a candidate being opposed by someone ineligible to oppose him or her is not harmed by the illegitimacy of the candidacy?