While a petition for a worker already in the H1B status is almost always accepted, there is still a chance that it doesn't work. There is a chance that it takes a long time to go through (usually a month or 2, but we're talking about the USCIS here :) ).

I changed employer twice with an H1B, and both times I made damn sure that the petition was approved before giving a notice (also, back then there was no official grace period, but I would have done the same).