[2021] can you escape with a pig's trap on your face?

If the trap was put on your head before the last generator had popped, then no you cannot escape the match via the exit gates without first taking the trap off - because it will be active.

If it was put on AFTER the last gen had popped then it would be safe to leave via the exit gates because the trap is not going to be active.

In all cases whether a trap is inactive or not, you can leave via the hatch.