There's exactly zero interaction between the default ATC and GSX.
Also, at the precise moment of touch down, GSX is not doing anything. To prevent stuttering when wheels touch ground, even if you pre-selected a gate in flight with GSX, which would normally trigger preparing it with all GSX vehicles at the gate, nothing is created when you touch down but, instead, the parked objects creation is delayed until your speed goes below 25 kts. If you don't pre-select a gate in flight, this won't matter, since GSX objects won't be created until after you select a gate with GSX after landing.
So no, there's no extra load at touchdown caused by GSX, regardless of if you preselect a gate in flight or not. That is if we are referring to the load caused by the extra objects loaded by GSX, which is the only time when GSX can (indirectly) cause the simulator to pause.
The other time when GSX needs to receive lots of data from the sim, is when entering the airport visibility range, since GSX will query Simconnect Navdata to get all data about the airport, which in case of large airports with lots of parking spot, it might cause a temporary increase in traffic over Simconnect but, obviously, it's not as if we could skip this step: how else would be able to know about parking spots and the taxiway layout ?
By default, the default airport "visibility" range is set to be a 3.0 NM radius around the airport center, but it's possible to change it, the manual has a chapter about airport visibility, of course. On a few airports that have a very large area (like EHAM or KDEN, for example) it's possible that 3.0 NM might still be close to the runway threshold, so you might try to increase the visibility range for these airports.
But it's not as if you are free to make it as large as you want: after a certain distance, which is about 5 NM outside the airport, MSFS won't load the airport jetways, so if you set the visibility range, forcing GSX to ask data earlier, if it's done before jetways are ready, it will cause the Navdata reporting the airport has no jetways. GSX *obviously* have code to minimize the issue, because it will query again for jetways after you reach your parking spot but, it's still not ideal, because assuming no parking has jetways would cause the GSX menu to show incorrect information so, there IS a reason why we set the default visibility range at 3.0 NM, you have *some* leeway to increase it, but not much.