The thing about the Borg Queen is, I think, the following:
The Borg Collective, the Hive Mind, is one single individual. That individual is represented by the Queen. She says to Data: I am the Borg. And as the Borg, she has always been lonely. Then she found Picard, who was about to be assimilated. But she wanted to make him more than just a simple drone so that she wasn't alone anymore. So in a way, he would have been a Borg King, but not quite.