fans are site specific usage. our back bedroom would never get warm in deep winter w/o them. and we have a very small house.
there is just a drastic choke point for the airflow getting back there.
but then some others don't need them at all.less noise, less fuss. i'm jealous.
if the basement is well insulated, the heat should warm the floors and radiate into the house.
i wouldn't underestimate the value of this until you try it out for a while.
*if* this works well when the stove runs for long periods you *might* get more time with no noisy stove running upstairs.
but that's a big house. these are just thoughts.
two stoves is a real luxury. if the fan helps with warm air already, you could keep both benefits, heat soaked floors and that basement stove also getting warm air up from the basement.
perhaps once the floors are heat soaked, you can run the lowest rate on the basement stove and still get a good result.
again, musings and conjecture here
edit to add - i have no idea which stove should be where in your situation.
it's a nice "problem" to have though.