Furnace left on while storing TT

Thanks for the info....Good and bad news I guess. The good is, we have 30 amp power at our deer lease where the trailer is being stored so I really don't need the battery....I was more worried about permanent damage to the unit which it sounds like it won't hurt it. That battery was slated to be replaced this year anyway so I may just wait until the weekend after next when we are already going out there. Question about the battery getting damaged....Can someone explain why draining it like this will damage it?

Also if it matters, the furnace we have is a suburban SF30F.