Yes...any FAA ratings and endorsements carry over...So if you have complex and high performance endorsements, then you can fly "complex" and high performance aeroplanes in G land. Same goes for tail dragger endorsement, ME RATING, etc....
NB: The RATINGS only carry across while the FAA ticket is valid...so if you let it lapse then they lapse too as you are using your FAA privileges without formality in a G reg - it is all in the ANO...