Does this actually work to coock it?

Doesn't seem safe to try to get your cock in it while it's in the hot spring. Maybe you could find a way to make it could actually work...but why? Are you a masochist or something?

Is it at all edible?

Sous vide method would probably have the most chance Of being edible since the turkey would be vacuum sealed

Is there any environmental impact or downside?

Yes. That's why the park service is saying not to do this. You'd be introducing new chemicals into a delicate ecosystem and also potentially physically damaging it.

It would cook it, the springs are hot and acidic enough. You’d just have to sit for a long while. Edibility depends on your allergies and tolerance for poisons.

Would depend on the specific hot spring. Most would cook and dissolve it. Additionally it would be very Sulphur smelling and tasting which would be range from icky to deadly depending on how much of the undissolved you ate.

The places I know were they do cook stuff using volcanic heat (in Peru and the Azores islands which are part of Portugal) they do it by digging a hole in an area were the ground is hot from volcanic heat and putting a pan cooking in it (they cover it all to keep the heat).

So it's more a local technique for cooking for free that then evolved into a couple of traditional dishes.

Never heard of trying to roast stuff on the output of a geyser.

Barrow Island, off the coast of Australia, is a class A nature reserve housing a couple dozen unique indigenous species, beaches where turtles lay their eggs each year, and 900 oil wells and a natural gas plant owned by Chevron.

Come and visit the stunning Yellowstone oil pumps

You wildly misunderstood my comment. I'm asking if this is actually a thing people have done which requires warnings from them. The Lego part is not the main thing. Like do they also have to post signs, etc warning people not to do this?