Currently, words/phrases globally filtered are prevented from being used in the initial hangman creation, both for the word to guess and the phrase. So yeah, this should be modified to prevent guessing globally filtered words/phrases too.
I also think we should prevent hangman creation or guesses with room-specific banned words/phrases. Ordinarily, we allow staff to bypass room-specific banwords, but given this is a hangman puzzle, if a staff member is making a hangman that is against their room's rules, then presumably regular users should be allowed to guess solutions against their room's rules, which probably shouldn't happen. Consider this an approval for both.