No, it will be there on the FBI record, the conviction cannot be deleted from the record like that, but the court will give you a dismissal letter saying that all charges were dropped, that court letter you will show to CIC. Also you need to explain what happened 10 years ago. You cannot hide anything, just make sure you tell the truth and all will be fine. If you lie, you will be denied.
Check with the court and find out if this record can be expunged or not because in some states you cannot expunge certain misdemeanors. Not expunging the records does not mean that you cannot apply, you can still apply, but to be on the safe side you should expunge the charge.