Yes. Most original NES, SNES, and Gameboy cartridges have probably lost their saved data by now, but the batteries can be replaced relatively easily. If I remember right, they're a standard type, like the ones used for watches or hearing aids.

I know that some my old NES games retained their data at least into the 2000s. Been a while since I pulled them out and checked.

Edit: I realize this article is talking about the game data, not save data. I don't know what type of memory older games used for the ROM or if it needs periodic power. I think the batteries were only for the writeable save data.