We have a wood stove, burned it a lot the first couple of years but not so much since then, it's really a backup for the main heating system.
We had a vent and fresh air kit put in from the wall right behind the stove, into the attic, and out under the eaves.
Once I happened to get lucky and was just checking on the stove and noticed the vent pipe was really hot.
I always check the draft before lighting it up, but I think the wind conditions were just right and it started drafting in reverse; I was lucky it didn't catch the wall on fire.
Since then I disconnected the stove from the vent and just have an open vent in the wall close to the stove.
Wood stove fresh air intake vents shouldn't, and have no need to, travel UP any distance, much less to the roof. They call that a chimney - and so it acted like one.
OP, there is no issue with a wood stove in a spray foam house unless it is truly too airtight to draw, which would be mitigated by the fresh air intake (vent) kit.