I expect it to be rare (if the wood furnace is doing its job), but only a test will tell.
The alternative is to run the wood furnace duct all the way over to the air handler plenum, but there isn't a good way to do that without dropping below the floor trusses...which I don't want to do.
Actually, another alternative would be to put a T in the wood furnace output just above the wood furnace, then install a normally closed and normally open electronic damper and wire it up so that with the air handler comes on, the wood furnace dumps the air into the basement until the air handler turns off, then it'd dump air back into the trunk. Basically, a "duct switch" so that only the air handler OR the wood furnace is feeding the trunk at any given time. More complex, but it'd work I think.