I don’t think that’ll do it. The propellant deflagration is so quick that the momentum of the drone means it can’t be accelerated backwards enough to significantly reduce the force on the airframe. Even if it did, that would just end up applying the acceleration to the internals such as the batteries and motors/engine instead. I think you would need a spring damper that would allow the weapon to recoil quickly and dissipate the energy more slowly, and I’m not sure you could make obe effective on something the size of a drone.
I guess you could, although the gripper would add a bit of mass to the drone. You still lose some energy from the round into the yeeted barrel, but not as much as having an open breech. Depending on the mass of the projectile vs the mass of the barrel that could be a worthwhile trade-off.