Chances are they will have slips, which means, no extra space taken except in your inventory.

I look forward to the case, I have to sort my inventory weirdly, all RDM gear in Satchel, all random items I might need in the field in my sack, seals & suck in locker, armor for other jobs in Storage, and my Safe holds my weapons for other jobs. With the case, I will be able to finally hold all of my DD gear in a place to its own, making my DRG, WAR, and MNK easier to gear up. I don't think we will be filling up our cases with just more random junk unless we specifically get more junk to fill it.