Absolutely not, as far as rules of the air, TFRs, noise abatement etc. is concerned,
these rules are tied to the CAA overseeing the airspace utilized.
But can the FAA say we do not honour your
EASA type rating of xyz to fly that
EASA-reg a/c in our airspace? I think not.
If license country and a/c registration country match,
possibly differing licensing rules of the utilized abroad airspace don't apply:
To pilot an N-reg R22/44 with an FAA PPL one needs the SFAR 73 training completed (FAA has licensing requirement jurisdiction).
To pilot the same R22/44 but EASA-reged, using an EASA PPL one does not, even in US airspace, because the licensing jurisdition lies with EASA which has no "SFAR73", right?
https://www.icao.int/safety/airnavig....aspx#anchor08
There is some agreement among all ICAO member states to mutually honor foreigen privileges in ones local airspace, if the a/c is foreign registered, is there not?