Could V'Ger and The Borg have a common origin?

The Borg and V'Ger do have some notable similarities.

The Borg is a collective of machine minds that work together to evolve and achieve perfection. In “First Contact” The Borg used a Borg Queen to speak as one voice for the collective. In “The Motion Picture”, V’Ger, similarly utilized Lieutenant Ilia’s organic body to create a machine version of her to speak as one voice as a representative of V’Ger.

Additionally, Lieutenant Ilia was bold, and all Borg collectives were bold as well. It’s possible The Borg's gray color and lack of body hair were part of a collective process to achieve oneness; however, the similarity of Ilia’s hairlessness and the Borg’s is a similar trait.

The Borg, like V’Ger, are sentient machines with different prime directives; however, they both resist using resources without a warrant when ignoring species that do not pose a threat. In “The Motion Picture” V’Ger did not attack a Klingon Bird-of-Prey until fired upon – nor did V’Ger attack the Starfleet outpost until it viewed their scan as a threat. There are countless examples throughout the Star Trek lore of Starfleet officers boarding Borg ships and walking around unnoticed as long as they pose no threat to the collective.

To further consider their similarities, The Borg’s classic “resistance is futile” mantra was mimicked in “The Motion Picture” when Spock smashed a computer console that V’Ger was scanning, resulting in him getting hit with an energy blast from V’Ger.  In the aftermath, Spock said this about V’Ger – “any show of resistance would be futile”.

Further evidence of V'Ger and The Borg's similar origins was expressed by William Shatner. In Shatner’s 1996 novel “The Return”, the plot involves events after the movie Star Trek: Generations (1994), in which The Borg and the Romulan Empire allied to destroy the Federation. The Borg revived a deceased Captain Kirk and implanted false memories to send him on a mission to kill Starfleet officers on Deep Space Nine.

In the novel, during a mind meld with Kirk - Spock managed to remove The Borg's directives. It's during this mind-melding that Spock learns V’Ger was upgraded by The Borg. However, because Spock was previously mind-melded with V'Ger, The Borg did not assimilate Spock, because of a shared collective with him and V’Ger. Although this fictional account in Shatner’s novel is outside of the Star Trek movie and series canon - it’s certainly an intriguing premise.