Hi 2Close,
Unless there has been a major change then I believe this still to be the case.
A couple of friends and myself did it the other way round (Got JAA PPL then applied for FAA on basis of), therefore our licences were restricted by our JAA licence and the FAA licence was in fact endorse which this. I.e. If you held a full FAA PPL then you are entitled to fly at night, however my friends has not done the JAA Night Rating as it was then and could there not fly at night, I had one so could. Therefore as everything is dependant/restricted by your 'base' licence you had to keep it current to keep your other current - NB: In the case of FAA based on JAA licence you still need to undertake a BFR even if JAA is current!
Since then I have added an FAA IR to the FAA PPL and finally went the whole hog and did the SE & ME Commercials - this means I can now throw my JAA licence in the bin if I want and my FAA licence is valid as it is now a stand alone licence.
Worth noting that despite what some flight schools will tell you, if you hold an ICAO PPL then you do not need to take the full FAA PPL course if you want to add an ME, IR or go for the CPL.