Most cyclocross races have tiers or classes. There's often an A grade and a B grade, right down to the Tyro or Noob class where the equipment requirements are minimal - in the order of "if you have a 2 wheel bike with working brakes, no obvious dangers, and a helmet you're good to ride in the beginner's grade"
For time reasons, sometimes the grades are run on the course together, so C grade and Newbies might mix it up, leaving the course nicely chewed up for the higher grade riders.
Locally there was a guy riding a raleigh 20 and the only difference was he had fitted knobbly tyres and removed the fenders for clearance. He didn't win but was not last, and he beat out nicer bikes too.
You can often even ride a mountain bike in a tyro-class CX races - The only thing often excluded is bar-ends.
If you're just trying out CX then go ahead and ride what you got. If you find that you like the sport then consider a better bike.