Hi, I put a very big electric 220v heater in my basement next to the on demand water heater so the pipes wouldn't freeze. It's a very old building and the water heater is right next to the exterior wall.

The main floor of the building is heated with propane. I'm being told that because the electric heater in the basement is not drawing cold air from outside it will increase propane consumption to heat the main floor. Is there any truth behind this?

Nope. Electric furnaces don't need fresh air, they only curculate air. They don't require combustion air like a gas furnace would. Heat rises, so I would guess you might even see less of a propane bill, but the electric bill will most definitely go up. Who is saying heating the basement with an electric furnace is going to raise consumption of the propane furnace? If the combustion air for the propane furnace is drawn from the basement, it will be taking that air and exhausting it out the vent, therefore more likely making the electric furnace run more, not the propane one, but either way, not enough to really notice a difference in the electric or propane bill. Hope this helps.