The pellet will precess, precession rates I estimate as about one cycle in 10 yards. This is a possible cause of pellet spiraling but spirals will be small. The effect of the precession yaw will be hidden by the down wind drift effect so will not really be noticed in practice.
The difference with a bullet is that its gyroscopic response will be different because it is aerodynamically unstable as opposed to a pellet which tends to be aerodynamically stable. The damping is also possibly better on many bullets giving a smaller effect for the precession.