Does GSX affect performance in any way?
The simple presence of GSX doesn't impact fps at all, if no services have been requested. When services are being called, the fps impact is the one of the models being called, which is roughly like adding a couple of AI airplanes.
is there any way to be able to install it to a FSX client computer to to run in network mode to keep the needed resources for GSX off the main sim computer.
There's no need to, because all the GSX script logic runs by the Couatl.exe file, which is the Python interpreter. Being a separate .EXE from FSX, it will automatically enjoy the scheduling of the OS so, on a multi-core system, it will use spare cores allocated by Windows. Since FSX uses cores to the fullest only when loading the scenery, it's fairly sure you'll have a lot of headroom to spare. This is the main advantage of Couatl compared to a .DLL module that would run in the same thread as FSX, affecting its peformances.