They stomp, only person that can make a difference is a competent stealth build Courier who proactively takes them out as soon as possible.
Actually, given the timeframe, the Courier would probably get killed pretty quickly. The best armor in the game won't really save him when fighting the Jem'Hadar.
The Changeling, if one is present, is quite surprised to find that Mr. House sounds exactly like Odo.
The JH go nuts and/or die out because of the lack of Cetracel White, I don't remember how that stuff affected them exactly, but they were hooked.
Also, aside for their advanced tech, the JH were not all thet good, so some beasties in the Mojave probably turn them into dinner.
That's why I suggested that the Dominion's first point of action is probably to develop the white that they need to keep the Jem'Hadar in line. They already know how to synthesize it and it involves using fungi plants. There are plenty of advanced biolabs in Fallout, specifically Big MT, which would probably have the equipment that the Dominion would need to synthesize a replacement before they ran out of their current stock (remember, they have white onboard the ships--probably several months worth).
As for the Jem'Hadar, most evidence suggests that they are exceptional soldiers. We know they regularly train and drill, we know they're aggressive, and will happily throw away their lives for their gods. Their shortcoming seems to be that they seemingly lack imagination, are not shy about killing subordinates for insubordination, and don't mind throwing away their own lives. The other large weakness, which you had already hit upon, is that the lack of white basically turns them into homicidal lunatics.
Jem'Hadar plasma weapons also have a disintegration setting too, so most monsters in the setting are going to die in rather short order, unless they're really fast and nasty, such as Death Claws.