No, Yojimbo's Cave is the "Cave of the Stolen Fayth". Mt. Gagazet has a cave that half of it has to be done under water (Rikku, Tidus, Wakka) so that must be what you saw referenced as "sunken cave"

There is also that blocked trail in Besaid which leads to the flooded cave where Wakka first asked Tidus to join the Aurochs.