Linking the Borg with V'ger for its own sake would be somewhat bizarre. They didn't have that much in common, and in a universe where all species look so similar to each other, casually linking two very different things won't feel right. V'ger's closest thing was Nomad, and the Borg are closest to the repair station in ENT: Dead Stop. I guess most viewers won't know about the repair station, but if anything is linked to the Borg's history, this is the closest match.
On the other hand, a good
story of focused on an experimental technology gone wrong that somehow leads to the creation of V'ger and the Borg at the same time would be awesome and creepy, I'd love it. And Dead Stop and Nomad stories could be seen as an example of how such things happened often, but without such disastrous consequences most of the time.
Unfortunately, I don't think this will fit as a plot for one of the films. Maybe a future series.