Yes. It will, providing your motherboard has compatible chipset/BIOS combo -- go to Digi's website at www.digidesign.com/compato for detailed compatability docs.
I'm running a Digi 001 on a PIII 550 MHz with 192 MB RAM (this is the minimum you need) and a 40 gig hard drive. Also, I'm still on Windows 98 SE. Works fine.