I'm starting to think no almost by definition but hear me out.
In the comments at pharyngula someone said this:
"That’s easy: no. You could be an atheist and not even be a naturalist of any kind. You could believe someone has psychic powers, for example, and not call that person a “god.”"
My problem with the idea of naturalism and ultimately the concept of the supernatural comes up in psychic powers.
We see psychic powers as supernatural because they break the laws of the universe as we understand them currently and there's no evidence they exist. This seem to be the 2 defining aspects of something supernatural 1. we couldn't currently explain something and 2. it doesn't seem to exist.
How do we know something exists? I'd say because it interacts with us or some other existent thing in a way we can observe. If something doesn't interact with anything else it is indistinguishable from non existence.* Some people claim faith as a means of knowing but ultimately faith relies on an absence of any evidence and is completely untestable, comparable or falsifiable so I don't think a belief in something's existence can in it self justify a claim of knowledge of it's existence. Certainly not to anyone else and I have doubts as to how convincing it can be on it's own to an individual.
So for the sake of this discussion lets say that a psychic power can interact with the rest of the natural either directly ie moving an object or somewhat more abstractly ie predicting the future. As soon as there is evidence they this interaction exists it will be unexplainable by our current science. However science is adaptable. This existence will cause scientists to reevaluate all natural laws and create new laws describing the limitations, and rules governing the psychic powers. When this is done the psychic powers have become part of the new natural laws. If they are now described by natural laws doesn't that now make them part of the set of natural things instead of the set of supernatural ones?
Even if we didn't understand the origin of the energy/power etc for the psychic powers it would be no different then our limited understanding of gravity. We can describe how gravity works but we have yet to distill out the exact causes of gravity. Gravity despite this gravity is considered natural.
If you look back in history this pattern seems to hold true. Things that have had claimed supernatural origins lightning, rainbows etc have been integrated into the natural the more we learn about them.Thus as far as I can tell the existence of a (colloquially) supernatural thing ultimately makes it natural. The whole idea of the supernatural seems based on things we currently understand can't and don't exist as far as we understand the world, when we do find them to exist they quickly become part of the natural.
*For a further analysis of this idea see Tracieh's dice model of existence, non existence and transcendence.
Easter bunny from wikipedia commons.