No you do not feel anything during a colonoscopy. A typical colonscopy is done first with the injection of a narcotic pain reliever. Then the patient is under local or general anesthesia.
During a conlonoscopy you are sedated and do not feel a thing, the hardest part is the prep which requires you drink a nasty medication to clean your colon.
During a colonscopy, the patient is sedated if not entirely asleep. The patient thus does not feel anything during the formal procedure. They may be falling asleep when the muscle relaxants are given.