I think that Casablanca makes the statement that human beings take sides and are defined by their choices. Complete neutrality in terms of refraining judgment and action on every point is impossible. When Rick says, "I'm the only cause I care about," or when he tries to relinquish any attachment to what is happening to Victor Lazlo, he strives to be neutral. Yet, in the end, Rick capitulates and does take a side. Interestingly enough, this statement extends to Casablanca, as a place. The entire setting of Casablanca is a neutral one. Captain Renault claims to be neutral, but acts with deliberate intent and is a product of his choices both as the narrative develops and in the "beautiful friendship" with Rick at the end. This helps to reflect how daily life in Casablanca goes on under the guise of neutrality, but where choices are made and sides are chosen. Even the cold force of business like Ferrari end up choosing sides. Ferrari ends up keeping "Rick's" as "Rick's" by employing Sam and the rest of the workers.
Neutrality is impossible in a place where neutrality is the Status Quo. Every human being on some level takes sides. It would be here in which I think that the film does conclude that to be neutral denies the essence of what it means to be a human being. All the characters depicted in the film take sides. This might not be reflective as much of the setting of World War II as much as the human condition. Complete objectivity is impossible. The contours and definitions of what it means to be a human being is one in which sides are taken. No one in the film can refrain from taking sides. Even Ilsa and Rick who live in a love that transcends the world around them must take sides when she is sent on a plane with Victor and when Rick says that what he must do is something from which she should be distant. In the end, to be a human being means to be defined by our choices and we become less than human when we are unable to do this. Rick becomes a human being only when his choices are made and his neutrality is abandoned, confirming the film's message that we are all waiting to become Rick Blaine when the moment presents itself.
When it comes to neutrality and the movie Casablanca, I've never actually thought of it from the perspective of what it says about humans. The idea of neutrality is expressed in the film mostly through the character of Rick, though also perhaps to a lesser extent Ilsa and Captain Renault, and Rick represents America during WWII. As America shifted away from the policy of isolationism and neutrality during the war years, we also see Rick depart from his neutral and rather distant behavior once Ilsa and Laszlo appear. I think the film itself expresses more a message of neutrality and the challenges that come with it, rather than what it says about being human itself.
However, to answer your question, I think it's a little difficult to say and more of an opinon, but I would answer no. The reason for that is because though Rick claims himself to be neutral, he has shown himself to be very much human. For instance, he helped the Loyalists in Spain and ran guns in Ethiopia. When soldiers sing a German Anthem at Rick's, he allows the band to play La Marseillaise to drown out the soldiers. Most importantly, at the end of the film, he allows Ilsa to escape on the plane, not with himself, but with Laszlo instead. If Rick is the symbol of neutrality like he thinks of himself, he has shown compassion and sacrifice that gives neutrality a human face. So with that, I would say that the film doesn't make the case that to be remain neutral is to be less than human.
At the same time, one could also argue that Rick's progression away from neutrality throughout the film is the cause behind his actions and his more human character. With that, the case could be made the going away from neutrality makes one more human, so therefore, being neutral would make one less human. Either way, to answer the question is a matter of how you want to interpret the movie.