Warships of that time, being entirely constructed of wood, didn't 'sink' but instead just settled into the water. Now that said, you wouldn't have flotation devices and if you were a marine in armour well... I've looked through my secondary sources and can't find any references to swimming so I've no idea the percentage who could survive in the water for some time. Although they could cling to the wreckage.

Now if the Romans won the battle, they'd be able to pick up the crews from 'sunken' ships as well as take those ships in tow to be repaired. If they lost, then likely death - warships of this type have very little room on board and keeping a mass of men on deck would hurt the stability of the ships. With the earlier (and smaller) trireme, the few marines and archers it carried were trained to shoot bows/throw javelins from a sitting position to maintain the ship's low centre of gravity. Fours and fives were larger but still, storing dozens of prisoners/future slaves on the deck would certainly affect the ship's seafaring capabilities. Why go through that risk? The damaged ships might be taken in tow since they could be repaired and crewed, but the enemy sailors would likely be left in the water.

Citing Greek sources, at Arginusae the Athenian navy was prevented from returning to recover men and ships by a storm - which led to a heavy loss of life and the prosecution of the naval commanders. From that we can extrapolate that recovery of the crews of 'sunken' ships was expected, especially since they were citizens. On the flip side, at the battle of Sybota the Corcyreans lost and abandoned their crews since they were mostly slaves, rather than acknowledge the loss (and ask their opponents for permission to recover survivors).