TL;DR Yes, see "primitive communism".
There is no NPOV answer to your questions, it all depends on your definitions and judgment of evidence. My answer is an attempt to explain things according to the point of view of Marx & Engels.
Full disclosure: I consider myself a communist.
According to Marx, the answer to the question is Yes.
To be communist, a society MUST be non-dictatorial - as dictatorship necessarily requires a state to control the means of production. If you do not have a means of coercion to control the means of production (army, police, etc.) - then you do not have a state.
"When, in the course of development, class distinctions have disappeared, and all production has been concentrated in the hands of
a vast association of the whole nation, the public power will lose its
political character. Political power, properly so called, is merely
the organized power of one class for oppressing another. If the
proletariat during its contest with the bourgeoisie is compelled, by
the force of circumstances, to organize itself as a class; if, by
means of a revolution, it makes itself the ruling class, and, as such,
sweeps away by force the old conditions of production, then it will,
along with these conditions, have swept away the conditions for the
existence of class antagonisms and of classes generally, and will
thereby have abolished its own supremacy as a class. In place of the
old bourgeois society, with its classes and class antagonisms, we
shall have an association in which the free development of each is the
condition for the free development of all.", Communist Manifesto,
Therefore it is a logical impossibility that there should be communist society that is dictatorial. Rather, the question is then: Has there ever been a communist society? If there has not been, then the answer to your question is No, otherwise Yes.
Communist societies have existed before the state ever existed, in the form that Marx refers to as "primitive communism"
Adding to the requirement of a stateless and classless society - in order to have communism, you must also abolish value itself. In Marxist theory, value is not the same as prince, and value is not the same as exchange value or use value. In Marx terms, value is the 'socially necessary abstract labor' embodied in a commodity. A commodity is any good or service produced by human labor and offered as a product for general sale on the market. To abolish value, you must abolish commodities and therefore markets.
@DVK is mostly incorrect, but @jvm is incorrect in other aspects too:
@jvm: Marx was certainly a Marxist, but said he was not as a way of saying, "if this is Marxism, then I'm not a Marxist" against the French communists & Paul Lafargue. Discussion on: I'm not a Marxist
Now to the few examples pointed out: Early christian communites, Kibbutzim, early workers' soviets (= councils) in Russia, The Paris Commune, Anarchism during the spanish civil war, particularly around Barcelona.
In none of these examples can we reasonably expect that the market or state was abolished as these societies either operated within a bigger picture where it was not abolished. In early Soviet Russia just after the revolution the market was certainly not dissolved. The Paris Commune was attacked and had armed forces. If you trade with places where the market still exists then commodities still exist. Anarchism during the Spanish Civil War was during a civil war - therefore they were fighting to uphold a means of production - therefore not communism.
The claim that @DVK makes that communism would somehow be an impossibility due to genes and how we evolved, i.e: "greed is in human nature" would require some scientific claims in the field of neuroscience and evolutionary biology. When it comes to biology, we are as genetically close to the violent chimpanzees as to the sharing bonobos that are the only other species except for us that uses sex for pleasure. One thing is for certain: cooperation is what made us the #1 apex predator species of the world. One human vs. one tiger is one well fed tiger. A few humans with tools against a tiger is a dead tiger.
One needs to remember that Capitalism had centuries to mature into the state it is in now - it had bloody revolutions, dictatorships, etc. One can't expect that the communist movement needs to honor "three strikes & you are out".