Not really, Gem crystals are formed over thousands if not millions of years under very specific heats and pressures in the earth's crust. The only real gem like that I can think of that actually exists is Amatrine, and that is formed when an amethyst crystal gets heated a certain way and part of the crystal turns into citrine. You end up with a crystal that is part purple and part yellow/green. They can be made artificially and are really not too expensive to find. But the thing is, it still is the same mineral (quartzite) not really what you are looking for.

The only practical way to do what you are talking about is to powder the gems and then suspend them in resin. You get a band made that is a channel that goes around the band and then have the resin set in that. This style of jewelry is very akin to the old enameled rings they used to make way back.