I think the overall numbers would drop, but it would still be disproportional to the "high crime" areas. People who tend to commit crimes are still going to commit them at a higher rate. Actually, the ratio might get worse since you would fall back to the basic murder, robbery, rape, and theft.
Would it, or would there be a lower "screw it, I'm already a criminal" factor? i.e. if you know you can get years in prison for having crack, you're not endangering yourself that much more if you steal to buy it.
Along the same lines as my theory that if guns are banned, plenty of folks, committing a felony by having them anyway, will go ahead and saw off the barrel of their home defense shotgun since it doesn't really add much risk.