I change my batteries every six months no matter what and have never had one go dead on me....but if memory serves, I had a battery go dead on another bass (not a MM) in 95 and the whole bass stopped making noise.
I'd always assumed that would be the case with my MMs, too.
I don't know that I've ever had the battery go all the way dead, BUT you should be able to hear a big difference in the tone, and out put volume as the battery nears it's end. If it seems like you have to turn your amp up extra high, or your just not getting the balls your use to out of the bass.. time to change the battery!
Just got a used 2000 Stingray 4 and the music store had removed the battery for safer shipping. When I had played it in the store a few days prior, the sound was full, but I took it out of the box and the case and the sound was weak...no battery. Popped one in and the bass sang.
Stingrays will operate without a functioning battery. All the knobs except volume will become useless, and the sound will be a little more transparent. Otherwise your bass should work fine.