Warranties are through the manufacturer, not the installer or installers company. If you buy a used car with a warranty you don't go to the previous owner of the car when something breaks, you go to a licenced service center/dealer.
Assuming the person offering the trade is a licenced installer (safe to assume IMHO, it would be prudent to check, but being able to obtain a furnace and then knowing how to install it would be highly suggestive of the fact) and they're operating on the up and up (so you'll get a receipt, even though it's a barter arrangement) I see no reason why warranty would be an issue.
I deliver to a few HVAC places and I'm reasonably confident that if I ever found a barter for something the owner wanted they'd do something similar in a heartbeat. The only difference is another item (vs cash) is being exchanged as payment, but the manufacturer couldn't deny a claim because of that.
Reality is that markup on HVAC is huge - I do know that because I've asked the warehouse guys in the back at the aforementioned HVAC places I've delivered at, so if an installer is getting a unit at wholesale and offering it up at retail-ish pricing for a trade for something he wants, potentially both parties win.
