Yes, spin increases your move speed (I added it to the description). It is not as clever as simulating spinning top physics or anything, you really just get increased character center velocity in a uniform way.
In the original design the boss tongue would spin faster and faster as to force the player to use spinning at some point but then it would also be less controllable and risky (e.g. hitting spikes or the bullets), but currently it doesn’t show off too much (because half of the bullets can be destroyed by the sword and the other half can be jumped over even while spinning).
Speaking of which, I will add to description that you can destroy red bullets.