No way. You have to UNLOCK them by doing the main storyline. I mean, who wants to see someont that hasn't even finished Survey Camp inside the Crab Empire?
If they don't allow you on Colossus Blvd without completing the other quests, why would they do so on Celestia? You won't get access to the new spells without completing each segment in turn, btw.
Personally, I'd like to see access to other worlds limited to Spiral Keys and no more porting, but dare to dream.