I think there is already a computer project like that --
http://www.chessbrain.net/

But to make it fair, Kasparov should be able to form his own "network"
of GMs!

Yes, the project Chess Brain exists but it's playing strength is not quite
what one should expect. In other words, Gary would mop the floor with it
time after time. Any strong conventional chess engine, as Fritz, Junior, or
the like, in a standalone monoprocessor computer, should do the same. At
least that was the last time my computer was part of the ChessBrain grid. It
has been some time since then, though, but I don't think its playing ability
has been improved so much.
Regards,
mafergut