Why would it need to be overwritten, though? The Jem'Hadar are perfectly capable of rebelling against the Vorta, or attacking Odo, or fighting their own kin, or devising their escape from the clutches of the Ketracel White addiction. Even if there remains some sort of vestigial respect of the Founders despite this evidenced freedom of operation, this doesn't stop an assimilated Jem'Hadar from waging war against the Dominion - unless the Jem'Hadar Drone comes face to face with a Founder, which would probably happen exceedingly seldom. After all, it's not as if the Jem'Hadar in Dominion service would be likely to meet a Founder even once in their life, either.
We have little evidence that assimilated humanoids would display their inborn characteristics. We haven't seen a greedy Ferengi Drone, or a cocky and sadistic Cardassian one, or a swaggering Klingon one. Drones just don't exhibit "behavior" of any sort much. It need not be a major problem to have a Jem'Hadar in the ranks, then: deep inside, he might have all sorts of strange thoughts about serving the Founders and earning back his life through victory and whatnot, but that wouldn't matter because externally he would be a loyal Drone under the guidance of the local Viniculum.
Timo Saloniemi