I had a sweep at 40+3, it wasn't painful, just slightly uncomfortable and it only takes a couple of seconds. Contractions started 24 hours later at about 10am on a Sunday, waters broke at 3am on the Monday on the way to the hospital and LO was born at 9am. It's unlikely you'll go into labour straight away, it could be hours later or even a couple of days.
I was quite happy with it because I was going to be induced on the Tuesday if I hadn't gone into labour by then.