If they want him to actually hold that office, sure. But that is an internal DNC process on how they do that. It isn't up to the Federal Judiciary.
If the Dems don't chose wisely, then their guy isn't qualified and doesn't get in, and the man who is qualified and has the most electoral votes gets in.
Competence and Judgement comes in question. The whole damn party closed their eyes to make a racial highwater mark. In attempting to do so, they drop a huge brown floater in the punch bowl, and are saying, “Drink Up”.