This answer will be rather brief: essentially it’s just fiction. In fact this would likely be the worst thing you could do to your ship during this period.

Our main source for naval warfare in the Peloponnesian War is Thucydides. We are repeatedly told that Greek triremes needed to be taken onto dry land to dry out the hulls of the ships. This kept the timber strong and avoided rot setting in. For example during the Siege of Syracuse in 414 BC the Athenian ships could not be taken onto dry land because of the fear of attack from the Syracusan navy and the need to maintain a blockade of their harbour. The commander of the forces Nicias wrote a letter back to Athens reporting on the dire conditions of his forces, and made an explicit point that “the length of the time we have now been in commission has rotted our ships and wasted our crews, and that with the entireness of our crews and the soundness of our ships the pristine efficiency of our navy has departed. For it is impossible for us to haul our ships ashore and careen them, because, the enemy's vessels being as many or more than our own, we are constantly anticipating an attack.” 7.12. Herodotus mentions Xerxes doing a similar thing with his fleet near Doriscus in the northern Aegean in 480 BC, and Xenophon says that the Spartan admiral Lysander (who you meet by the statue of Leonidas in Sparta in the game by the way!) hauled his fleet onto dry land at Ephesus towards the end of the Peloponnesian War. This seems to be a necessity to keep the ships battle ready.

Ideally therefore triremes and other ancient battleships would be brought onto the shore for careening - the hull would be given time to dry, any damages can be repaired, barnacles and other marine growth can be scraped off. The hull would also be caulked and coated with pitch to help make it watertight. As at Syracuse any long term action in the water without this careening would rot the wood and make the ships unusable. If they were to hide their ships they often did it overland, for example the Peloponnesians would often haul their ships over the Isthmus at Corinth to try and avoid the Athenian fleet.

Therefore if Barnabas were to intentionally sink the Adrestia for hiding, if they left it too long they either would have nothing left to pull up or what they did recover would be beyond salvage for action.