Yes that will work to stop the vibrating. But you better think about it real good first. Because while this will stop the ducting and drywall from making the noise hitting each other, it will work by bonding them together. What this means is any mechanical sound or vibration in the ducting will be transmitted to the drywall. If its minor you might not notice even up close. But you could just as easily wind up turning the wall into a speaker that lets you hear really good all the furnace air noises and believe me you do not want that! Only you know how loud your furnace is, how close, etc.
But the alternative really good and proper fix is remove the drywall, secure the duct real good, install insulation, and replace, refinish and repaint. That's a lot of see's. Vs one small hole you plug up with some plaster and are done.
If it was me I'd try the hole. That gap filler really expands a lot. Don't drill, use something like a 16 penny nail to poke a hole. That way it will push the duct and not cut through like the drill bit might. Maybe even blunt the nail first. Push the duct back as much as you can, to create some volume to get more bond area. Then just blast it in there. Should work. Fingers crossed!
