I don't think having a finished Zodiac weapon will result in a huge benefit for progression, though Yoshi's statement to that fact was somewhat vague so it's still a possibility. I'd imagine we're more likely to get something cosmetic.

My original line of thought was akin to yours, that the 3.0 relic questline would begin with the Zodiac stage, meaning those of us with Zetas would already be a little bit ahead. Given the recent revelation that the new jobs will not have Zodiac weapons at all, though, I'm not so sure that will be the case now. Chances are we'll see a new type of Relic entirely (perhaps Mythics reborn, if they follow the FFXI naming conventions).

What we might see, if they do intend to give us a slight progression edge, is the ability to transfer our Zeta's stat configuration to the future relic, though, so that we don't have to go through whatever new stage they put in to customize the new one. I would be fine with that.