No. They were originally conceived as an insectoid race, the remnants of that storyline you can see as the space bugs in the episode Conspiracy.
Budget constraints kept the Borg from being depicted as insectoids as
Maurice Hurley had originally intended, though the hive concept
survived to become the overwhelming group mind known as the
Collective. Q-Who
It's also mentioned that the impetus upon introducing what would become the Borg was simply a new enemy for our heroes to fight.
This was intended to lead into a series of episodes that would have
introduced the Borg as a main villain in the wake of the Ferengi's
complete failure to meet with audience expectations of a major
Starfleet antagonist. Q-Who
It's pretty clear that later stories about Borg, at least on TNG, while dealing with a multitude of themes, came about simply building upon what was started in Q-Who, and then building on what came later. You have this implacable new enemy you want to see again but ultimately without a direct foil for the heroes. So you make Picard the bad guy and send him on a wave of destruction, only stopped in the nick of time. So then you've done the ultimate Borg show, you can't top that. So you don't, you make a small personal story with just one Borg and give it humanity. And so on. Until you get to First Contact, where you change them into space zombies or vampires or something.
If anything, I feel the utopia of the Federation represents the idealistic worldview of a post-scarcity hybrid democratic/communist state. The Borg don't really represent a political ideology, more like some kind of societal change of the ultimate integration of self and technology, possibly what writers were prognosticating at the time all the way back when, but the future we seem edging towards.
