Running Furnace on Low Battery?

EEWally wrote:
What would happen if the furnace was needed while the battery ran low or became discharged (no AC connection)?

Your question is moot because you shouldn't ever be drawing down your battery anywhere near as low so as to cause the furnace to not ignite. Generally, you want to draw the battery down no more that ~ 50% capacity or ~ 12 volts on a regular basis, drawing down to ~ 30% or ~ 11.75 volts occasionally is considered acceptable as long as it's not done often and you re-charge as soon afterward as is practical. These voltages aren't anywhere near the low threshold voltage for your furnace OR your fridge to not operate.