First Cyclocross Race - Riding a Mountain Bike
Many first time cross racers use a mountain bike. It makes perfect sense, don't go out and spend $1500+ before you even know whether cyclocross is your cup of tea. Most all races allow mountain bikes, the only type of equipment that's usually forbidden is a fixed gear.

A full suspension mountain bike will do just fine as an introductory race vehicle. Your primary setback is that it's heavier than a cross bike, so it will slow you down when carrying it up a steep incline, or carrying it over the barriers, etc. But, those beefy ( and heavy ) tires might carry you through the mud quite nicely, maybe even putting you at somewhat of an advantage in a muddy beginners race.

Just be friendly and courteous out on the course, cyclocross is about having fun.