I would believe that CCW would have exactly such an effect.
Here's my guess as to what will happen: some specifications will show that CCW decreases crime, others will show that it increases it, others will show that it has no effect, and all will be equally plausible.
That's why I think Gary Kleck has the right approach to the gun control debate. Trying to figure out whether gun rights (CCW as well as others) on net increase or decrease crime is a fruitless excercise, so arguments should instead be based on principle.