The furnace will be perfectly fine running unattended... It is designed to safe to run when the unit is occupied, even when sleeping.
Now there are some issues.
Battery power will only last a short time, unless it is plugged in.
Propane last awhile, depending on the temps, both inside and outside. But is won't last forever.
I often leave my TT at a dog trial for a week or so, in freezing temps. I make sure it's full on propane, set the Tstat at 55 or so, and ask someone to run my generator a few hours every day.