As far as I am aware, it has never been tested. Clearly he should not be able to run, and clearly neither should Trump, but laws only have meaning if they are enforced.
[edited:] That's what the Trump cases in MN etc are about. The MN(?) judge punted, though, and declined to say whether he was ineligible for office, saying instead, basically, that the state didn't have any rule against insurrectionists being on primary ballots.
Parties are welcome to nominate someone who might never be allowed to take office - that's a party problem, not a state problem.
The first thing I thought of was the Trump crap, like is this guy just going to be the first one ousted then there is precedence for Trump to be ousted as well?