Yep, I'm confused, I missed that the stove is on the main floor and not in the basement.
OK, lets see, you need to pull air from the basement to hopefully get some of the warm air on the first floor to migrate down the stairs to the basement. So I guess hooking into the cold air return that pulls air from the basement would be a way to get air out of the basement. But you will need to cover the other grills to the return duct or you will be pulling air from all over the house, not just the basement.
I hope this makes sense this time.