Obviously the Borg are their own thing, but the encounter itself seems too similar to have not been influenced.
I came across this same thing in another thread just the other day -- the idea that something is too similar not to be an intentional influence. The truth is, since different creators are all drawing on the same pool of cultural referents and precedents, different works of fiction and art coincidentally resemble each other all the time. It's actually very hard to
avoid accidental similarities to other works -- the primary reason why episode pitches to TV shows or submissions to fiction magazines get rejected is "We're already doing something like that."
Really, the trope of being held paralyzed in an energy beam fired by some vast ship can probably be found in many places throughout science fiction, going back to the pulp era. The
Millennium Falcon and the Death Star spring to mind, or the abduction of the heroes' plane by the Metalunan saucer in
This Island Earth. Within Trek, you could also cite V'Ger's tractor beam holding the
Enterprise, and no doubt others. It's a pretty basic trope, tying into universal fears of being helpless in the face of something gigantic and powerful. The reason so many works of fiction resemble each other is because fiction is made up of recurring tropes that carry meaning to the audience.
As for comparing Balok to the Borg based solely on being uncommunicative, that's a hell of a reach. Balok communicated quite a bit, in a dominating, bullying way, as part of his test/intimidation. The Borg just gave a single rote announcement and otherwise took no interest in the crew. And of course both had totally different natures and intentions. So I don't see a parallel there.
So no, I have to disagree. There's no reason at all to suspect anything more than a coincidental similarity. All they have in common is one trope that can be found in a number of other science fiction works.