It depends on the drugs used, the individual response to the drugs and the time under sedation. In conscious sedation you are never really ‘asleep’ although it may seem so. The patient can be aroused by verbal command or physical stimuli.
Recovery is swift after the infusion of drugs is stopped. You could feel drowsy or light headed for a period after the procedure. In deeper forms of sedation consciousness is normally regained within minutes of the discontinuation of the drugs.