Depends on the privileges that you want. The FAA test at each privilege unlike EASA who grant blanket coverage across certain classes. So doing an FAA ATP on a 737 will not grant you CPL/IR privileges on other classes. If you just want to fly a 737 then the ATP written and a check ride will grant you that. If you want CPL/ME/IR privileges then you will need to test for those as will you if you want to fly SEP.