If you have to carry your bike at all (for a run up or barriers) the weight of the mt bike will be a liability, OTOH the singlespeed category will probably be all of the singlespeeders and will likely include very advanced riders.
If the course is mostly flat the mt bike may be more of a liability too. My cross experience is relatively limited, but I did find that as a road biker I was able to fly by the mt bikers on the flat sections (especially the paved one....), but my off road technical skills (especially going down) were not nearly as good as them - so it was a game of lets keep passing one another...
On a hilly or technical course a single speed may not even be that much slower than a geared bike. One of my teammates often does both races (she's a cat 2 cross) and generally finds that her lap times are only 10-12 seconds slower on the single speed - which tells you how much of it is handling skills.