No, just different, artificially created, levels of the same mind. They are not billions of voices working as one, they are billions of voices forced into submission by some undefined force.
The Queen has stated very clearly that she IS the Collective, not rules it, not controlls it, she IS it. She might just be an avatar for the Collective as a whole, or like I said before, the will of the orginal Borg species. Notice how neither Picard nor Seven are aware of the Queen until they face her outside the Collective? Possibly because she's not an individual entity but something more.
But in the end it remains, the Borg are not what we thought they were and while we don't know what exactly that is it is not exactly a dictatorship either.