It should give you a message when starting up your game, something like:
"The internal battery has run dry"
"Clock based events will no longer occur"
I've had a fake Sapphire (sold it for 25 bucks, the poor sucker didn't know he couldn't save, LOL) so I know..
Anyway, you should check if you've got the real game. Is the game cartridge colored in a translucent green (Emerald), translucent Blue (Sapphire) or translucent Red? (Ruby). If so, you have the real game (and nothing to worry about), you can just send it to Nintendo.
Although it depends on where you live. If you live in russia (considering your username), it might be hard. I don't think there's a Nintendo of Russia.