Does a swing-slide frameless glass door mechanism exist?
Expanding on my comment: I think that the main problem with the proposed setup is lacking a slide or rail on the bottom. Without a slide on the bottom the glass door can swing perpendicular to the sliding direction. See the below explanation for what I mean.

I have a sliding shower door with a sliding mechanism on the top (a stainless steel rail with 2 wheels per door on top of the rail) and a tiny U channel on the bottom to keep the door from swinging. I know, I need to clean the shower a little...



The door is sliding in the direction of the blue arrows. The U channel on the bottom is keeping the door from swinging in the direction of the red arrows. This U channel is about 2 CM long and seems to be made from aluminium.