I'm hardly an archaeologist, but I can pretty definitively answer both these questions: almost certainly not, and absolutely not. While we have thousands of known shipwrecks from the Roman Period in the Mediterranean, we have exactly zero warships from antiquity. This should not be surprising in the slightest. During the Roman Period the Mediterranean was by far the most active center of sea trade in the world. The shipwrecks that we have represent an insignificantly small fraction of the total trade ships that plied the Mediterranean. Fleets of warships, though quite impressive on paper, made up an eensy weensy little speck of all naval traffic, and the chances of ever finding one are next to none (though archaeologists still hold out hope!). Further, warships were significantly less durable than their trading counterparts. Warships in antiquity were built for combat, and combat alone. They were not particularly seaworthy, often could not handle damage well, were topheavy, didn't have enough room for provisions (so they had to be beached to allow crews to forage), could not be trusted to remain afloat at night (and so had to be beached at night)...you get the idea...A warship wrecked in battle would almost certainly not survive, and the places we expect to find warships is by the coasts and in harbors. Moreover--and this is getting at the first question--where would we look? We have a general idea of where some naval battles took place, but there's a lot that happens between a ship going under and its hitting the bottom, even without worrying about the extremely slim chances of its preservation. Currents will carry a ship all over the place (especially in this particular example, since these ships were lost in stormy weather!), conditions at the bottom might cause the wreck to end up not directly below the spot where it sank, ships will break apart as they sink, etc. And our textual references, which is the only way we can find the locations of such wrecks, are rarely good enough to be able to even get a half-way decent idea of where to look. We know more or less the exact location of, say, Salamis. But Salamis took place in a narrow strait, and there are natural boundaries indicating the widest possible points at which combat might have occurred. We have nothing even remotely approaching that for most naval battles, and finding the location of a fleet lost to storms would be a nightmare of pure conjecture