Well, yes it could, and it is, with the GUI. The notation is superfluous for me, for playing here on Gamerz.
By way of comparison, the current center of mass system would be much more difficult to use with a real set.
If you are concerned about an easy to use notation system for physical games, then a double coordinate grid, perhaps similar to what is used for Trax, would be one solution, awkward looking or not.
I don't see Tantrix listed on the Gamerz help page. Andantino is listed, but it's strictly pbem, not GUI. How do players make moves in Andantino?