I did two CX races on my old Trek 660 last fall. That's basically what I did: fit the fattest tires I could (which happen to be pretty much the thinnest CX tires you can find). Worked great for the dry and dusty September race:
Not so great for the muddy November race.
The brake calipers just jammed with mud and I had to stop a few times to dig it out. Not optimal. I think I may have to save up a few bucks and find a proper CX frame on eBay for next fall.