Well, first you have to define how much faster is even theoretically possible. On a fresh XP install you should be able to run Darwinbots with >99% of the CPU. So it's not like windows is stealing CPU resources that other OSes might give you back. I'd consider it more an issue of users running Darwinbots on a "dirty" windows install, with lots of programs running in the background that eat memory and CPU. If you're running servers where you want to dedicate the hardware to run Darwinbots, any windows version should work just fine and it becomes more an issue of licensing problems (windows installs cost money).
But that's strictly theoretical. You might get totally different performance from different OSes running Darwinbots, I can't say for sure. But I'd be surprised if any differences exceeded 5% at the outside. And if they did, I imagine it would have more to do with poor thread scheduling dirtying caches than one being magically faster.
So ReactOS might be good from a strictly "it's free" point of view, but I doubt you'll see any performance improvement.
