Yep you can get a complex endorsement, even if your FAA licence is issued on the basis of your UK PPL. I have a UK PPL, no NR, nada, but have FAA Licence issued on basis of my JAA PPL, FAA IR(A), FAA ME (IR) and a complex endorsement. As the complex endorsment is simply an endorsement in your logbook by an FAA CFI, then once endorsed, this limitation no longer applies. With the IR and ME your airmans certificate is maked with "US test passed"....
You can do the FAA skill test if you want, but you'd be wasting your money...