Combining Game Genie rom with game roms?

I've been searching everywhere to find out if it is possible to patch an NES rom to also include the Game Genie rom and start up just as if a real GG was plugged into an NES.
I know there are easier ways to bake codes into a game, but I prefer the flexibility of adding/removing codes at will. Also, this is for my (S)NES Classics, which normally requires any GG codes to be backed in before uploading to the system. I don't want permanent codes and would prefer to do it the old-fashioned and authentic way... I mean that's kinda the point of these mini systems for me, bridging that gap between nostalgia and convenience.
So yeah, is there any way to append the GG rom to an NES rom so that the game boots to the GG rom and then to the game?
Thanks for any help... Made an account just to ask this question!

Just appending a piece of code to a ROM doesn't cause the code to get run. You have to patch the ROM to jump to the code, as the GBA-era warez scene intros used to. And even if the menu runs, the writes that the menu makes to configure the interposer circuit won't have any effect unless the emulator supports the Game Genie. The emulator in the NES Classic Edition and Super NES Classic Edition does not.

Yeah, I had a funny feeling it was way more complicated than I'd imagined. Definitely a shame, would've solved my problem easily.

It'd be easier to use (or write) an emulator that always loads the game genie rom before the rom you picked, instead of accepting the codes externally and then loading the rom directly.

There's some multicart pirate boards that are capable of showing a menu before choosing a game, but they don't have game-genie patching capabilities.

Well, except for maybe PowerPak / Everdrive N8. Those are capable of this, but obviously that's not something for an .NES ROM.

I don't think there are any existing iNES mappers that would help you get this into a .NES file. You can apply game genie codes as a patch directly to a ROM file, if you want, but not really the runtime menu thing. I do think there are emulators that will let you use the Game Genie ROM in tandem with another ROM file though.

Kinda interesting that on computers it was super common for crackers to add a cheat menu intro screen. They could get away with it though because everything was loaded into RAM. Much harder to patch a ROM. You could actually do something like this for an FDS game, potentially.