It depends on what you consider "similar", but no, the rotation of the paper has nothing to do with the rotation of helicopter blades during autorotation. In that case, the blades act like ordinary wings and they do an ordinary glide, albeit in a circular direction because the blades are fixed at one end. What happens with the paper is different. The axis of rotation is horizontal rather than vertical.

However, there is a sort of rotation about a horizontal axis in an ordinary wing because a wing produces vortices, and this is a necessary part of the process of producing lift [1]. In heavy aircraft these vortices can be surprisingly powerful and long-lasting, to the point where they can cause smaller aircraft to lose control and even crash if they get caught in one [2].

That first reference has an excellent description of what was going on in my design [3].

[1] https://www.av8n.com/how/htm/airfoils.html#sec-circulation-v...

[2] https://en.wikipedia.org/wiki/Wake_turbulence

[3] https://www.av8n.com/how/htm/airfoils.html#sec-spinners