Not really, some enemy´s can swim even with deeper waters, and some seem ? to walk on the seafloor (saw few skeletons from the event spawning on the mainland and the next time i look over from my island they are on my beach).
Also as far as i now there is a limit on how deep you can mine down, but i have not tested that below waterlevel.

If you want to stop random spawns nearby you will need to place workbenches.
Place a workbench and a stonecutter if you have it and then make a stonecoffin around the workbench, tear down the cutter, move to the edge of the workbenches radius and repeat till you coverd enough of the land next to the island.
Stakewalls are also an option, as long as the monsters dont see the workbench they will not attack.
But sometimes mobs could still walk into the area, or follow another monster they are attacking.