Is there any reason that plumbing can't be adjacent to a heating/cooling duct?
In my experience, there are at least two things you should be aware of.


Running hot and cold water lines will cause the water temperature in the lines to change a lot quicker than ambient. The actual distance of the run and distance between pipe and duct will affect the effect. When my air conditioner is running, the hot water gets cold within 15 minutes since it's last use and then requires running the water for an extra minute or two to clear the lines. The opposite is true for the could water when the heater is run. This is really only a minor inconvenience, but a moderate inefficiency.
A floor vent in a room with running water will eventually flood, even if it's only a small spill or leak. The water will run through the vent and eventually come out in an inconvenient and unexpected location. The moist duct will collect lint, then mildew or mold and will be a pain to get clean.


Because of point 2, I would strongly recommend raising the duct and vent at least an inch proud of the floor around it.