They would have tried, but with no new source of ketrucel white, they would have died in a few weeks. And with no brain to guide them and no fists to impose their will, the Vorta would have posed little threat.
It would depend on when the Founders' destruction happened, since there actually was a new source of Ketracel White established somewhere in the Alpha or Beta quadrant. See below for more detail...
Did it really require the founders to make the Ketracel White? I thought the Vorta, possibly with some technicians of some sort, could operate the factories that made it. The Vorta would probably have been just as eager to take as much of the Alpha Quadrant with them as they died as the Jem Hadar, aside from occassional defective clones like Keevan.
Early in the Dominion War, there were repeated supply issues since they were limited to Ketracel White brought all the way from the Gamma Quadrant. According to Starfleet analysis, it was apparently impossible to replicate the stuff. The recipe and manufacturing process were probably closely guarded by the Founders.
But somehow, later on they were able to have the Son'a start producing the stuff en masse on this side of the galaxy with at least one new facility, as revealed in that unforgettable masterpiece Star Trek: Insurrection and later confirmed in the DS9 episode "Penumbra." And maybe there were more new facilities besides that one. So presumably, at that point there would have been a continual supply of Ketracel White even if the Founders' planet had been blown to smithereens.
Kor