Shower curb tile: OK to caulk rather than grout?
I would not use caulk on this. Grout provides strength to the tile, especially the corners and sides. Using a unsanded epoxy grout would be your best bet since it's waterproof and doesn't need to be sealed. It can also be used on plane changes, vertical to horizontal surfaces. Caulk never goes on as smooth as you'd like it to whereas grout does. It will probably be faster to grout than caulk and unlike caulk, the grout will probably last as long as the tile.