The hours flown as training will count towards an FAA only licence PROVIDED they are either;
Flown with an FAA rated flying instructor if within Federal airspace, or
Flown OUTSIDE Federal airpsace if flown with a JAA only rated instructor.
I'm guessing you'll be in Federal airspace and with an FAA rated flying instructor - but for ****'s sake PERSONALLY CHECK the individual licence of whichever flying instructor your chosen school puts you with.
DON'T just take the schools word for it that the instructor is rated in whatever flavour you need them to be.