I know that some glass/crystal faceted beads are dyed after cutting, but are there any that use colored glass, e.g. Swarovski beads?
Yes, there are solid-color glass beads where the color you see is present throughout the entire bead and will not fade or wear off. The color for these is added in the beginning of the glass making process so it is in there for good. In the Fire Mountain Gems and Beads® catalogs, these items are marked with this icon:
The solid color glass beads include round beads in range of sizes and a rainbow of colors, as well as some Swarovski crystal crystal and Celestial Crystal® glass beads. Some Swarovski and Celestial beads, especially those with effects or finishes, are not true color. For these, like Swarovski's red magma, the base color is crystal (clear) and the color you see is a coating.