I'm going to say that your biggest hurdle will (1st) be the clearance "under the fork" and (2nd) inside the seat stays (as Clifton says). The brake calipers can usually be upgraded for more clearance at a reasonable price. Clearance problems with the fork would normally require an upgrade. The rear stays, on the other-hand, can sometimes be carefully indented for more clearance.

I run Kenda Kommando 700/32s on my track framed S.S. CX/Urban/Hybrid lash-up. These tires easily clear everything but "under the fork" (which only clears by ~ 6-7mm). This, of course, limits its ability to run in anything more than light to medium thick mud. I'll also add that I'm happily using a pair of $40 USD Tektro R730 (BR7308) Long Reach Road Calipers w/ Kool Stop mtb pads. YMMV

Btw, you might ask those that are holding the race about borrowing a CX bike just to see how you like that style of racing. That way, when all goes well, you can either modify your "old roadbike" or buy/build a dedicated CXer.

Good luck on your first race!