I was figuring that since this was a Rental, its installation might be regulated otherwise.
In any event, as 'bc' said, I wouldn't throw any ductwork in with any other existing ductwork that's meant for 1 purpose. I would think this would be a hazard if done as you wanted. Go ahead with your temporary solution but I have to wonder how much this shack is being held together with spit and chewing gum. I'm not saying that you need to treat your rental (or your Renters) as your own home (or your own Kids), but I guess they're knocking down the door to rent your place. Sooooo, short-cuts as you describe are OK. Because, if they aren't knocking down the door to rent the place, I don't think your new 'feature' would be much of a selling point. As a renter, myself, for over 15 years, I didn't mind paying good $$$ for a place that was worth paying good $$$ for.
Anything temporary, like what you're proposing to do, doesn't say much in one respect. (You can tell I'm not a Slum Lord ...) 'Nough said.