V'ger was actually linked to the Borg by the Great Bird of the Galaxy himself. Roddenberry implied a connection in an interview IIRC regarding TNG and the episode 'QWho'. It's obvious STO has paid homage to this with the sector block Red Alert events. EDIT- Although it is possible Roddenberry was joking in that interview.

Remember TMP was pretty vague about it. Spock had a brief mind-meld, it's entirely possible he only got a fraction of V'ger's history or only parts of it could be interpreted. A planet full of 'living machines' could easily be interpreted as a planet full of Borg. We don't know, because we never see it for ourselves.

To address the OP, I don't think Q or the Continuum had anything to do with the formation of the Borg. But it is one of Star Trek's biggest mysteries. Among many, really.