No.
The battery dead means you can still play the game, but the game won't save, and will corrupt the existing game.
This probably means the game itself became corrupted. It happens sometimes. I would suggest getting a new one. Used G/S versions are cheap at EB Games.
But I wouldn't give up hope yet. Does your GameBoy work with other cartridges? If not, that's the problem.
Still, when i've had that problem, I blew in the cartridge and the slot in the GB, and after a bit, it worked.