No, a light wave packet does not have a group velocity that mimics a corkscrew spiral. The group velocity of a wave packet refers to the velocity at which the overall envelope or "group" of the wave packet propagates through space, while the individual waves within the packet propagate with different phase velocities.
In the case of light, which is an electromagnetic wave, the group velocity of a wave packet is always equal to the speed of light in vacuum, denoted by "c." This means that the overall envelope of a light wave packet moves through space at a constant velocity, perpendicular to the direction of the corkscrew spiral you mentioned.
The corkscrew spiral pattern you might be referring to is typically associated with the phase velocity of a wave, which describes the speed at which individual points of a wave (peaks, troughs, or other points of constant phase) move through space. However, it's important to note that the phase velocity is not directly related to the movement of the wave packet as a whole.
In summary, while individual waves within a light wave packet may exhibit a corkscrew-like pattern associated with their phase velocities, the overall group velocity of the packet remains constant and parallel to the propagation direction, following the speed of light in vacuum.