It will depend on your production. When I did it, we had an automated wagon for the office and winched wagons and fly pieces for the other scenes. It is a rather quick show (ours was 1 hour 25 minutes) but it has 8 or 9 scenes, each of which requires a scenic transition. Father Flynn does have a quick change, and our production didn't have a lot of hand props but did have a ton of dressing in the office. Even with all the transitions our tech still flew by and went rather smoothly once we got the timing of the office wagon down.
It's a very emotionally charged piece for the actors, so just stay alert of their needs throughout the rehearsal process/run.