We're not comparing Zack to AVALANCHE as a whole, only Tifa. Without Tifa Cloud would neve rhave left Nibelheim sure. As a result he never joins Avalanche. Thus, Avalanche never goes after Sephiroth, or if it does it fails.
But interestingly enough if we take Zack out of the equation, Cloud still doesn't join Avalanche.
Zack's importance is roughly equl with Tifa's importance as an individual during the main course of the game. Just cause a character doesn't do much, or anything really, during the main events of the game does not mean he/she is not vitally important.
No it isn't.
Zack saved Cloud's life? So what?
Tifa is responsible for this:
Inspiring Cloud to go join the military and attempt to become a hero.
Spurring Cloud's desire for vengeance and giving him the extra push to put down Sephiroth.
Participating in numerous pivotal moments and battles in the story.
Pointing out all of the discrepancies in Cloud's memories.
Leading Avalanche in Cloud's stead before relegating the role to Cid to take care of Cloud.
Saving Cloud from the influence of Sephiroth and his tainted memories, rekindling his will to live and save the world.
Participating in the final battle.
Helping Cloud establish a normal life, reminding him he's not alone and establishing a proper support family for Cloud.
Zack saved Clouds life and was there to experience the downfall of Shinra's greatest heroes. That's an important role, sure.
I don't feel as though that makes him as important as Tifa, or really any of Avalanche. They're the heroes and stars of the series, so of course they will be more important. Zack is a support character.