Yes, I'm sure it can tie into the story. Brink is about two forces who are morally ambiguous; each believes they are on the right side and only want to do what's best for the Ark. Two armies fight each other, etc. Then zombies just come in, throw any notion of a plot out the window, and make it a cheap survival mode instead of competing against other players.
And for your Borderlands comparison...the zombie add-on for that had the exact same gameplay as the regular game (in Brink the gameplay would have to change) and while Brink is going for at least a sense of believability, Borderlands has you fighting Skagzilla and "Bad*** Psychos."
I like zombies as much as the next guy; played every Resident Evil, I've played Borderlands with the zombie DLC, Left 4 Dead, Killing Floor, etc., but we don't need it in every single game.
tl;dr
Borderlands zombie DLC didn't change gameplay; Brink zombies would change gameplay
Borderlands is supposed to be as insane as possible; Brink's plot tries to maintain a sense of realism
Zombies are overdone.
My argument for zombies consist of:
A large sum of people like zombies, and would purchase the game because of it.
Adding another mode to the game could only add to the fun, taking away NOTHING from the other story modes.
(In which case if the zombie mode built on the main story mode, it would go for both good and bad sides. It could be an end to a certain smaller gang war where they band together and fight off the zombies)
But I've yet to understand what you all mean by adding zombies would change gameplay? Would would still have to use teamwork to advance, just like in l4d or killing floor. The zombies could be really aggressive for example, putting your team into a helping frenzy. And it could still include doing objectives for all classes. (In the case that your team is being pushed back into the map further.
I can see how people can dislike the idea of zombies, but if you do dislike it, just choose not to play it. Plain and simple.