If a user has been suspended on ***any site*** in the entire SE network, then they are ***currently not eligible*** to run in an election anywhere in the network until at least 1 year after the suspension is over: https://meta.stackexchange.com/q/274114/391772.

After that 1-year period is over, PolyGeo is correct that ***past misdeeds are forgiven.***. However, if you are concerned about that user becoming a moderator because you think they are likely to do the same suspension-worthy thing again, then you might be happy to know that they would lose their diamond if they make insults related to peoples' nationality again.