From Dr. Robert Brill, Research Scientist Emeritus:
I have never heard anything about such a process.
To become "sealed" is not necessarily to be "compatible". If a diamond were to be enclosed within a glob of molten glass, after the glass set up, the diamond might become sealed in the glass in the sense that it could be "encased" in the glass. However, the diamond would not be sealed (bonded) to the glass, as would be the case when one piece of glass is fused inside another piece of glass. Also, the coefficient of expansion of diamond is only about one-tenth that of ordinary glasses, so it would not be considered "compatible". For example, if a diamond was encased inside a set-up glob of glass, the glass would be strained for some region surrounding the included diamond. (The glass immediately surrounding the glass would probably be in tension.) Whether or not the glass could tolerate the resulting strain without breaking would depend upon all sorts of variables — the size of the diamond relative to the volume of the glass, the coefficient of expansion of the glass, whether or not the glass was annealed properly, etc., etc.
The diamond would probably behave much as any other highly-refractory "stone" in a glass. (Stones are imperfections trapped within glasses. They can be caused by incomplete melting of batch materials, the accidental inclusion of impurity minerals in the batch, crystallization of the glass around tiny nuclei in the glass, or bits of refractory materials broken away from tank walls or crucibles.) In the case of a diamond, the diamond inclusion would probably remain visible because the refractive index of diamond is quite different than that of most glasses.
