All you are going to get for your foreign ATP is a FAA private certificate limited to "VFR only" under 61.75. And the FAA guidance says the foreign license has to be "valid." A letter from the Orlando FSDO says "valid and current." All of the limitations of your foreign license apply to your 61.75 certificate. One example the FAA gives is a German glider pilot getting a FAA glider rating based on their German license. Since German glider pilots must have a valid medical certificate, the FAA glider rating based on the German license is void if the German pilot does not have a current medical even though the FAA does not require glider pilots to hold a medical certificate.
In order to have instrument privileges added to to a 61.75 certificate that allows instrument flight, you must take a knowledge test of FAA instrument rules, the Instrument Pilot Foreign test. Or you can go the full route under 61.65 and get a FAA instrument rating, in which case your certificate will say "US Test Passed."