Cyclocross - Cross Bike on a Criterium?

I am thinking about riding in some criterium (road) races. My road bike has a relaxed geometry -- the write ups and reviews all say "this thing is excellent for long, hilly rides, but just don't take it to your local criterium."

Instead of dropping serious cash on a more race-specific road bike, I'm thinking of riding my cross bike with slicks in the criteriums. I've ridden it on the road with slicks before, and it generally handles well (with a small and occasional fork chatter issue on some big decents if I use the top-mount levers, but there aren't big decents on criteriums). The higher bottom bracket should be good for the tight corners. Tire clearance, cantilevers with top-mount levers, and cable routing all seem to me irrelevant.

Has anyone tried it? Am I setting myself up for a big crash (or poor performance) based on something I'm not seeing here?

If you do badly, it'll be because of the motor not the bike. Just give it a shot, there's no sense in spending a lot of money if you don't know if you'll stick with it.

Criteriums are fast and furious races, with tight-knit packs of riders diving into sharp corners at speeds approaching 30mph. I think it would be a good idea if testing this kind of riding out for yourself on your CX bike (with slicks) on your own in a parking lot to see how confident you feel going full-bore into a sharp corner, leaning low, and sprinting out. Criteriums are all about bike handling skills, so experiment for yourself and see if you can trust the geometry of your CX bike to safely carry you around criterium-style cornering; can you drop it into the corner quickly, can you lean low and fast, can you straighten it up afterwards and sprint away?

I've seen it done before in fact by a pro last year right after cross season (not sure why he decided to use it). Actually the higher BB is worse for cornering because it's better to have a lower center of gravity. But like jpearl said if you are comfortable bombing through corners in practice than the cross bike won't be a terrible disadvantage.