There is siliconized tile grout that is touted to be waterproof but I'd check with a tile expert before I pinned my hopes for longevity to it.

I'm no expert but... grout doesn't do much: 1. fills the variable void between tiles and 2. is acceptably aesthetic while filling that void.

There are colored caulks in a wide pallet of colors that are intended for use in sealing against water around sinks and counter tops. Check with the counter top folks at some big box or builders supply houses. They will probably NOT have a clue as to using it as a grout substitute but can at lest supply the stuff. The stuff I got was in squeeze tubes to be used by hand (sans caulking gun.)

I would think a good silicone caulk could be used in lieu of grout to avoid water ingress and the EVIL freeze thaw cycle. After all you will probably not be walking on (or dancing on) that table top.

Please post some pix as you progress.

Pat