...I'm trying to imagine Picard in an actual zombie outbreak, trying to argue for their rights and being diplomatic about it xD
Depending on the "type" of zombie we're talking about I doubt Picard could argue for rights. Though you've just given me an idea I might knock out for some Halloween "fan fiction" with zombies (classic Romero type) invading the Enterprise.
But on the bent of "largely mindless drones mostly only bent on propagating their species through a form of contact" Borg fit a very wide definition of "Zombie."
Sure the Borg *do* have "an" intelligence and a means to their end in what they do (where as Zombies typically have neither) but they're both still gray, slow-moving, beings whom you don't want touching you.