Yeah, they write to nvram I believe on your system.
When you play online it completely factory restores the (roms) system so that everything runs correctly, like it is one machine.
Moes cheats are loaded by both players at the start of the game and the host resets the machine, which temporarily loads them to memory for that kaillera session. Close, desync, crash and you have to do it over.
If you know what you are doing it takes less than 10 seconds to do though, unless you are playing someone without the cheats.