Can you disconnect the island using Cast Down into the Briny Deep?
Yes. For instance, if you sink the middle board in the "Coastline" layout variant 3-player game, there are now two island boards left. By default, there is no way to get from one board to the other, but
if you want (player option), you may treat lands that were Range 2 from each other before the sinking as still being Range 2 after the sinking, per the Archipelago rules.
(This can be annoying to track, which is why it's not a mandatory rule.)