So recently been playing hawk on turn 6 when limbo is active and the game ends.
Same with playing it into deaths domain on turn 6 with other cards to win that location.
Tried it onto bar with no name and it briefly turned in my favour whilst the cards turned but when the game ended it flipped back despite hawk being active.
Not sure if it's a bug or just the way bar with no works.
Anyway for science!
I did the same thing earlier. The effect ends at game end so it would revert back just before scoring. At least I think that's how it works.