Well, you COULD... But ultimately just doing the legwork is just a whole lot more efficient. However, we have things to speed you along on your merry way in the Guild Vault, like Dragonbone weapons (these scale with level, so they're the best thing ever for leveling new alts to level cap).
Things to know:
1) The profession you need the most is Leadership, put all your focus to it. Wild Slop can hit you up with some goodies on loan that you can use to unlock two extra slots to speed this up.
2) Invoke every day once you can. First, you'll want to just get the 6/7 Celestial Coins campaign chests though, and use them to build up campaign stuff for Sharandar (it's the first campaign, and the most tedious even with maximum lazy bastard efficiency, so it's helpful to come prepared).