I have some experience with glass, and I don't think it's a suitable substitute for a stone as something set into a ring. I don't see rings being made with "beads" either, in fact I'm a little confused by that. Earrings, necklaces, but rings? I suspect that the fingers are too busy and vulnerable to keep the glass from breaking. Eric might have more to say, he's a jeweler.
As for getting glass made on the playa...I know people do do glass on playa. I even have a piece that I got in 03 or 04. It came from some sort of furnace and I didn't get to see it being made; I assume that they had done it the day before and annealed it over night. And even at the glass bead level, I'd go with annealing, unless you're dealing with boro-silicate... You don't want a piece that gets left out in the sun and shatters because getting it hot causes the hidden tension in an annealed piece to shatter. But annealing requires a kiln, with a controller, so that's electricity, always dicey on playa. And it requires supervision, i.e. not running off after something pretty, or go bar hopping or whatever. Not that there aren't glass makers who are that dedicated, but I wouldn't rely on finding one. And even before that, they have a torch, which means propane--no problem--and O2--problem. I'm not sure if it's even legal to transport that without a license. And the torches (unless they are using MAPP gas, which is kind of like using a thirty-year old subaru with three cylanders instead of a v8) are expensive pieces of equipment. As are the kilns--most especially their electronic controllers.
I'm not saying it's impossible. I wouldn't count on it. Maybe there's a plan b that would work. We can bat around ideas.
The Lady with a Lamprey
"The powerful are exploiting people, art and ideas, and this leads to us plebes debating how to best ration ice.
Man, no wonder they always win....." Lonesomebri