I somehow doubt the Founders physically manufactured the White themselves. The Vorta had to have done that being they were the ones distributing it.
Tain just didn't think it through... at all. In all likelihood the Great Link, albeit smaller, would've survived between the ones actively infiltrating, the hundred and any who may be in the Dominion doing anything else.
Regardless, the Vorta would unleash the Jem'Hadar, even if they somehow were all annihilated. The Female Founder In What We Leave Behind flat out said the Jem'Hadar would fight to the death, even after she died. I somehow doubt the Vorta are just going to stop making the White just because their gods are dead. If anything quite the opposite, they'll want to avenge them.