The only problem is that instead of re-circulating and filtering conditioned air, a furnace fan is going to bring in external unconditioned air (and is only filtered once).
I’ve never seen a furnace fan that pulls in outside air, unless it was some DIY garbage that wasn’t to code, or a huge money waster from 100 years ago.
Most older homes simple have an outdoor draft/damper for makeup air.
You’ll draw in a lot of dirty outside air with that setup if you don’t block/reduce outside air intake. It will still go through a filter, but it’s going to cause the filter to dirty very quickly.