I have need to work with the ZX40 and decided to test run ZBasic under WINE on my Linux box. It appears that the compiler and IDE work quite well. I haven't had a chance to work with the actual chip (that will arrive soon enough ). I'm also looking at writing a native ZLoad for Linux. No offense but I have limited access to Windows.
I don't know how old your distributiion is but I suspect that it should. The version of WINE I'm running is 0.9.25. Fedora FC 6 is fairly recent. The good news with Linux is that despite the distribution it's still Linux underneath and I know how to manipulate that to make lots of programs work.