It will still be possible its just that the regs will change to state that the instructor has to have a JAA or what ever the new setup is Instructor rating as well as a FAA.
So there is nothing stopping a company, and I presume OAT will continue training over there, training as long as they can find instructors suitably qualified with both systems.
What it will mean is these instructors will be in quite short supply until things get themselves sorted out. The normal cut and thrust of flight school operations will be slightly changed as the supply of instructors will be way out stripped by demand. So it may mean that T&C's of the instructors will be improved which will be fed on to the customer.
I have a sneaky feeling that things will be quite confused for a period until things sort themselves out. I should imagine it may get quite political for a period as FAA instructors will see a reasonable chunk of business in thier areas suddenly disappear to be done by Europeans who will be getting paid more than the FAA guys.
I suspect they will start playing difficult with greencards and it will end up that the Irish passport holders will corner the market.
There are other ways of doing it ie train for a FAA license then convert it to a JAA one.
I can't see it stopping though, there are some right devious bastards running the JAA schools in the US. I am sure they will find a way around any restrictions the regulators impose.