No no no. :P
The Borg Collective is a single giant mind. It's spread throughout all of the drones, just like our mind is spread throughout all of our brain cells. This mind is the Borg Queen. The body we saw played by Alice Krige and Susanna Thompson is just a puppet that the mind controls.
There's no royal family. For my take on why the Borg wanted Picard, have a read of my free novelization of The Best of Both Worlds, Part One, chapter four. A link to it is in my signature.