When are you able to trade with GameCube games? Trying to get all 3 Hoenn starters with only one copy of the game

I’m trying to complete a Gen III dex on original hardware, so I need to be able to get all the starters. I only have Emerald and Leafgreen, which can’t trade with each other until after the E4, so I can’t just trade over and reset, and I don’t want to play through the entire game three times.

I think I could use my Pokemon GameCube games as an intermediary, where I just trade the starter over to Colosseum or XD, reset, and repeat until they’re all in my GameCube, then trade them all back to my GBA. Would this work?

My understanding is that FRLG won’t be able to trade with Colosseum/XD until getting the National Dex and completing the comm network quest, so for Charmander/Bulbasaur/Squirtle I’ll just have to borrow someone else’s copy of the game. I would prefer to not have to do this for Emerald.

My main question: For Emerald, are you allowed to trade over Hoenn Pokemon to GameCube before you’ve gotten the National Dex? I’ve seen conflicting info on the Internet and can’t tell for sure. Would I be able to transfer my starters to GameCube right after starting the game (assuming I have enough Pokemon to trade and have Pokeballs)?