The Save File Will Be Loaded Pokemon Emerald
The save file in Pokémon Emerald is stored on a non-volatile flash memory chip. This chip does not require a battery to retain data. You could remove the cartridge battery entirely, and your level 100 Swampert would still be there.
If you see the message when booting up Pokémon Emerald , you are likely holding a counterfeit or "reproduction" (repro) cartridge . the save file will be loaded pokemon emerald
Since Emerald does not need a battery to save, replacing the battery only restores berries growing, Mirage Island appearing, and the tides in Shoal Cave. You can ignore the battery dry message completely if you don't care about those features. The save file in Pokémon Emerald is stored