The "recoil" is angular, a torque impulse, in the opposite direction of the spin. Also, as Tom says, it occurs at load or spin-up, separated in time from the release. There would be little or no recoil at the moment of release.
There could be considerable vibration when loading, but if the projectiles distributed evenly in chambers around the circumference, there need not be a lot of vibration when loaded but not firing.