Doesn't sound plausible - at some point players will be done hunting for BST collections and then new players won't have a full synced party in the FATE to get their BST collections as easily - Party Finder could work but it's different from being able to queue a data-center into a duty as the FATE requires you to be there on the spot with no guarantee on spawning. FATE could just as well time out before a full party of BST gathers up.
Even if people do show up on these Hunts, there's no guarantee they'll be running BST or BLU or another job entirely.