Whether Dem voters got to vote in the GOP run-off or not was probably a function of the election procedures of the particular county in which they were registered. If MS is like the rest of the places I’ve lived, some counties are very careful to check information, some aren’t.
I’m not sure how many irregular voters he actually needs to prove. The margin of victory was about 6,000 votes in the run-off. I don’t know if that means he has to prove 12,000 votes were illegal (because theoretically, the illegal votes could have gone either way) or just find enough to prove that the election was seriously tainted by the illegal votes and thus get it thrown out.
You are correct, hence my distinction between possible and probable.