I'm not sure it would be considered recycled smoke. It is just taking a little longer to get from the main smoke box to the cold smoke box.
It is a very popular method in home built smokers to run the smoke for a distance in a tube underground before flowing into the smoker. So, unless you were talking about somehow recirculating the smoke from the top back through the bottom again, I don't know that I would consider this recycled.
My thoughts anyhow.