[philistine]

You're right that the save is going to vanish from the batteries, but tests and anecdata have shown that cartridge batteries on Game Boy can easily last more than three decades.

Pokémon Silver, Gold, and Crystal have a clock inside the cartridge, limiting their survivability to around a decade.

[jdiff]

All Gameboy games (as far as I'm aware) have batteries inside the cartridge, the saves were stored on volatile memory and were battery-backed. Gold, Silver, and Crystal just made extra use of the battery with an RTC. I can find many instances across many forums of people talking and troubleshooting replacement batteries for their Red cartridges so I don't believe my memory is failing me here.