The pre-requisite for an FAA ATP is either an ATP or Commercial Pilot's License with Instrument rating issued by an ICAO contracting state. So a "frozen" JAA ATPL would meet that requirement since technically you hold a Commercial with Instrument.
You would however, have to go through all of the aeronautical experience requirements for the category and class of aircraft you want to get your ATP in and make sure you meet all those requirements. Google FAA FAR 61.159 (or just look a few posts up from this one and it's quoted for you) and that will get you to the aeronautical experience requirements for the ATP airplane category rating.
You would also be required to pass the FAA written test and practical test.
Last edited by raysalmon; 2nd Apr 2011 at 07:09.