A crossbow would be better. If you can do some metalwork you can fashion one out of a VSR 10. I actually have Drawings for one,might even have some CAD plans.
You could just use an actual bow and put a barrel where the arrow would go, and then a separate tube parallel to it with a plunger system attached to the string.
So letting the string loose blasts air into the barrel via the parallel plunger type mechanism.
Basically,yes. You can use an A&K SVD cylinder and a pistol barrel to keep the overall length low. Hide the innards in a big steel tube with cutouts for the bow string to attach to the piston.
There used to be a device called an airbow. Long piston attached to the string in a cylinder attached to the bow. It fired small darts allowing practice at home. airsoft cylinders are not long enough, you need about 2 ft draw length. Think long thin bicycle pump bolted halfway along it's cylinder to the bow. With a pistol barrel maybe mounted on top. I would add an O ring in front of the bb so the pressure can build up before it shoots.