I don’t have too much familiarity with galaxy 2, so sorry if this is a stupid question. Is there a cheat code that could be used to start the game as Luigi, or is that impossible, and if so why?

There is a ROM hack, but it is not the base game so it isn't allowed

There is one, see the resources. It won't be allowed on here, but if enough people run it we could always have a category extension or romhack board :)