ROM injection as the technique would likely be known tends not to be done for GBA games, though most things represent either a serious porting effort (something like Phantasy Star collection) or had far better emulators in homebrew (most NES efforts) so that is not entirely surprising. On later systems where devs wrote better emulators than homebrew types cared to compete with, or initially cared to compete with, (usually Nintendo consoles but not always) you also have the incomplete emulation issue where only what is needed for the games in question is emulated and I don't know enough about 2600 coding to know what the pitfalls might be here (though "more art than science" would be a phrase I expect to hear back about coding for such things which also does not help for emulation).
Also had a quick look for 2600 emulators for the GBA. There were apparently some proof of concept things ( https://web.archive.org/web/20110502151659/http://www.taswegian.com/TwoHeaded/2600.html
) but nothing ever went too far that I can see. Later systems had a bit more though so might be worth looking at those. Afraid I never really investigated them (StellaDS for instance for the DS, and the PSP has a few things) but I see good things written so maybe there.
Anyway. The best case scenario is the 2600 ROM is directly stuffed into the GBA ROM with a bunch of its mates and the GBA section is the emulator, any saves/high scores (which might cause a problem) and selection menu.
Slightly more annoying is if said ROM is compressed or treated in a different way to "Scene"/mame/standard emulator practices for a given system. Sega was somewhat infamous for this at points but interleaving issues, bank arrangements and whatever else present options for things to be jumbled or a few bytes off here and there which brings it all crashing down. Though once you figure out the pattern then it is sorted easily enough.
After this we come to the emulation tweaks world. Here graphics might be prerendered in GBA formats, some kind of high level emulation used to emulate the game logic rather than the system, and any number of other things that boost performance over what a native emulator might be able to pull off.