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: Let's disallow moderator nominations from people who've been suspended in the past year.
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.