Unless you can figure a way to filter furnace air or even just their ducting, you will have whatever dust enters the basement storage area. My DW constantly complains that 10 minutes after she has wiped everything down, some of it's back. As a matter of fact, even that cold air return will let any basement dust in but if it's anything like our HC, you can pull the vent covers (on the step risers or the forward wall), an make up a filter from one purchased at any hardware or big box store.
A ponderable - why is an RVs a/c air (kinda) filtered and the furnace air not
? Hmmm