I doubt any connection between V'ger and the Borg. For one thing, V'ger considered all organic life as "infestations" and machines as the only true lifeforms, whereas the Borg deliberately seek out life to assimilate, then there is the incongruity of the detailed elegance of the Ilia probe compared to the haphazard and clunky functionality of Borg drones, if the Borg came from V'ger then something went horribly wrong between the time of their creation and the first time the Federation encounters them.
I've always envisaged the Borg as the result of an experiment in nanotechnology that went horribly wrong, or the creation of some mad scientist type that let loose her creation on an unsuspecting populace, becoming the first queen and template for those who followed.