Yes - One piece of paper. The BP itself has no meaning, it's the bar code printed on it and that will get you from origin to destination even if you do have an aircraft change. Same thing in IRROPS, whoever rebooks you will simply issue a BP for the new flight. In theory, one physical piece of paper could contain your entire RT itinerary.

While the BP should be fine at PHX if you need to exit security, I would feel more comfortable asking the GA for a gate pass for PHX to avoid delays at checkpoint. Also, given lines at checkpoints at PHX, I would not exit sterile area unless a genuine need.