With velocities of the pellets being sub 800fps at the muzzle, the shooting would have to be very close.
Even a .410, if open choked would have worked really well on those close birds.
I've shot grouse on the road with my choked .410, using both 1/2 oz. loads and 3" loads with what, 11/16's ounce #6's and had the birds fly off. Range maybe 20-25 yards.
I'd rather head shoot them with one of my air rifles.