I have heard of it being done.
An average hunting arrow weighs in the neighborhood of 400-500 grains,an 1 1/8 ounce pellet load in a 12 gauge weighs 492 grains,so if you pulled the pellets from a trap load,and somehow got the arrow attached,it could work.
Such a gizmo would be used at fairly close range,if you experimented ,you could probably figure out some type of fletching,or maybe use a muzzleloader,with the shaft in some type of sabot to impart the rifling spin,a heavy weight,large diameter arrow shaft,long enough to keep the broadhead out of the barrel,some type of plastic sabot,to seal the bore ,and keep the arrow centered in the bore....I think it would work.
If somebody wants to front me $10,000,I could come up with a working prototype.
I have seen ramrods fired by accident without any damage,other than generous recoil,but those had a bullet and the ramrod.