In case you are not yet convinced about the inadvisability of such a visit, I'll add my experience. We had to visit the Uffizi on the free Sunday, because it was our last day in Florence. (We had been misinformed by our guidebook, and tried the afternoon before, when it was closed.) The crowds were so dense that if you stepped back to get a better view of a painting, the space was immediately filled; and you could see nothing. This was in late December. I can only imagine it would be a zillion times worse in Rome near Easter. Actually, having been in Rome the week before Easter, and having visited the Vatican Museum then, I can tell you that the crowds will be pretty bad even at times when you have to pay.