Seems like the guild storage is there so that when a person reaches different milestones in the guild academy, they automatically receive the item from the storage.
EDIT: Existing members of the guild cannot enroll at the academy. I've tried with my alt... O__o There's a separate Academy chat tab but I'm not sure if only the guild master is able to see it or if the whole guild is able to chat there as well. More things to figure out.
EDIT2: The rest of the guild is able to see academy chat.
Woot.