Ujm, if they become frum they will at some point be checked out, certainly before they are married. If they don’t, then being in the yeshiva hasn’t helped or harmed them in terms of intermarriage, because while whoever they marry might think they’re Jewish, if they or their children ever marry into klal yisroel, there will be a bedikah, and it will not harm the klal.
I personally know a case where a boy thought he was jewish, but it turned out thar his maternal grandmother converted through reform/conservative. The kid was learning full time, he was 20ish, and underwent a giur immediately.
If you’re worried about yayin nesech, bishul akum, etc while they’re not observant, then the same halacha applies(mostly) to secular jews as well.