I seems inevitable that a movie tie-in, even a modestly successful one, will boost a show for awhile. If the movie is marketed well, and widely accessible, this will be particularly true. However, POTO is, and has been, a big tourist show. It had high percentages even before the movie. It's been running for 18 years. IMO Rent is not quite as big a phenomena, though it's doing solid business. Rent, because of its subject matter, may also not have quite the same mass-market appeal.
"And the postman sighed as he scratched his head, you really rather thought she ought to be dead..."