I mostly agree with DW and Almandrigal in re: don't queue if you're busy, but it would be fine to add this if it were implemented reasonably.
It doesn't need to. Make it so that anyone who's paused the queue can only advance as far as queue position #2. If a person in party has the queue paused, nobody in the party can advance ahead of position #2.
For everyone else skipping over the paused people, it would be little different from when you're in a roulette, and a duty would-pop except you don't have access to the specific duty, so it offers it to the first eligible person in queue instead of you. There is no pileup there either.
This is easily handled by capping your pause time to 5 or 10 minutes before it either A) ejects you from queue or B) force unpauses your queue.