No, you only get loyalty in single player offline. I think the best way to build up points is to run a load of perfect laps and zones in Zone mode. I prefer my custom EG-X skin to the unlockable skins though. That said, some of the other ships seem easier to use when they look different (e.g. Icaras concept), even though they're exactly the same really.
edit: Probably best to get 100000 loyalty for 1 ship, because this unlocks all the skins for all ships.