I guess the question is flawed, because Rubik's Cube is a static puzzle (starting from a given position) and not a dynamic, two-player game that is more of a game theory issue. Assuming the best possible moves (like when two computers are playing against each other) it still boils down to the quality of "move-dialogue". So, the answer should be "It depends..."

http://www.vanheusden.com/cchess/datamining_on_chess.html

Here the average number of moves comes to: 57.63. (Humans, both sides;  "Humans Number")

As a fellow sub-20 speedsolver since last November, and also a starting chess enthusiast, I would have to say that it was already complex enough to find God's number on such a simple concept (programming and code-wise) as a Rubik's cube with computers. The number of positions for chess is exponentially giant, and I think that computers for chess cannot help us very much more (such as for openings and such), but that isn't to say that chess playing computers can't get stronger. I believe that computers will continue to get even stronger, and their search depth will just become too superior for humans to contend with.