This is a great idea, I love playing chess.
The problem with playing for Bitcoins (or any kind of money) is cheating. If you play with someone, you can be running a Chessmaster copy in the background and just make the moves that the computer does (by using your opponent's moves against your PC). This way your opponent would always lose, unless he is Kasparov - or unless you are playing blitz chess where there is no time to use the Chessmaster. Correct me if I am wrong.
Just bet very small amounts if you are afraid to lose. You may lose some bitcoins, but it might worth the chess lesson.
There is no cheating as long as you don't pretend you are a human being. Kasparov himself is an advocate of "advanced chess", where players are free to be assisted by computers.
And even a computer-only network would be interesting (for it could give some nice chess games). Chess programers could compete for bitcoins and it might still be fun.