GSX cannot cause pauses when leaving the airport, since it doesn't create anything and it doesn't do anything, except checking which airports are around you, which is not something that can pause the sim, since it's done in the background without creating objects (only created objects can pause the sim) with the code running entirely outside the sim.
Nobody else reported this before. It's normal you would have a pause at the parking, when all the GSX objects are being created, but not when flying.
However, in order to be sure of this, I tried a departure from JFK with the PMDG 777, and couldn't notice any pause: just the 777 that halved my fps from about 45-50 with a default airplane, to about 20-25, but no pauses I could see.
However, I departed from a random runway, so it might be useful if you could say which runway you departed from, which direction you took, and the approximate location where you had the pauses, so I could try under the same conditions.