The answer is yes. From my experience, you have
to have 
..an exemption by the State to allow you to fly.
Now, if everything was in accordance with ICAO, everything, then you would not.
As an example, airports in the US meet FAA standards, not ICAO. The FAA can approve a US based carrier for RNP. The FAA cannot approve a foreign based carrier, as the airport would have to meet ICAO standards, and the FAA would have to use ICAO RNP design parameters, per the Chicago Convention.
Canada's WestJet tried to get the FAA authorization to use the Palm Springs RNP procedures, but could never get the OpSpec because of the Convention.