Kinda/sorta.
The way receptors work is that the ligand (opoids in this case) attaches and activate the receptor, and then leave and the receptor deactivates. Rinse, wash, repeate. It's a fairly random process in the sense of, short of a massive concentration of ligand relative to the receptors, not all of the receptors are going to be activated at all times.
Now throw in a competitive inhibitor such as naloxone. Prior to administration, the opoids are coming and going from the receptor site without any trouble. Once narcan comes in, it also starts coming and going from the receptors, just without activating it. Since you can either have an opoid or a naloxone molecule at the receptor, if naloxone is already there, the opoid can't activate it. Similarly, once the opoid molecule leaves the receptor (which it will do with or without the naloxone), naloxone is free to come in and cover the site.