John, It is 2013 so if this model is from 2006 it is about 7 years old:-) Time flies when you play with toy trains.
The PS-2 3V system is more battery friendly. MTH makes a charger that you can plug into the bottom of the tender to charge it. Or you can leave it on the track to charge, though I would turn smoke off, and volume down. Set voltage around 10 to 12 volts.
If this is truely at 0 volts, I think it will take longer to charge up. If you are operating conventionally, the engine will start up but probably not come out of neutral when you try to change direction.
If you are running DCS it should run fine, just won't be able to store any changes on shut down, since the battery is dead.
I would recommend changing the battery to the new green version. The 2.4V batteries had a life around 5-7 years. G