Although I think it is a long-shot in the worst sense of the word, I believe that most tech-savy people are looking for the best price/performance ration. If Cyrix has come up with the Duron-killer, then those who know and understand IPC and FPU performance will probably buy it. That is of course making whole mess of assumptions such as stability, good mobo/chipset support, etc.
The problem w/Cyrix won't be fighting brand loyalty, those on a budget are forever pragmatic, but rather the long battle for respectability, accessibility, and compatibility that AMD has been waging. This is what will lead to an increased market share.
I am certainly wishing Cyrix the best of luck because the more competition the better, as far as I'm concerned.