Adding a simple relay

The only caution I would give you is that the pellet stove may short cycle because the operation is a littler different and the furnace may heat the space before the pellet stove has time to contribute it heat to the space.

What brand pellet stove?

There are remote thermostats for pellet stoves that eleminate wiring.

Personally I wouldn't tie my pellet stove to the furnace.

You might be surprised what would happen if you changed your thermostat to a one with a recirculation feature that turns on the fan for duration of time every hour. Just running a pellet stove. I heat my house with two pellet stoves through the winter and recirc the air.