Not at all. Theoretically anywhere on the Earth is a valid archaeological dig site depending on what you're trying to find, and our current understanding of how humans spread out across the world relies on the very fact that global water levels were lower historically than they are now.

That said you do highlight the other problem- salt water is the bane of archaeologists. For anything to be preserved well it typically needs some form of phenomenon to halt the growth of bacteria and be free of caustic or acidic substances. A mudslide preserved an entire village over in the state of Washington (http://en.wikipedia.org/wiki/Ozette_Indian_Village_Archeological_Site). Otherwise you rely on things like tar pits, bogs, or human intervention (EG: Mummification) to basically halt the growth and exposure of things that'll eat away at the artifacts.

If I remember correctly, /u/vampire_seraphin is a flaired user in underwater archaeology. If you don't get a response here, you could PM him/her. You may also be interested in this profile page.

It's my understanding that historians and archaeologists suspect that there are a lot of post ice age settlements currently under water just off the shores of the Mediterranean, the British Isles, etc. The receding glaciers melted and sea levels rose, submerging incredible amounts of fascinating evidence of prehistoric civilization.

Sure. Coastlines change all the time and structures are lost or abandoned. The same goes for campsites, midden piles, shell deposits, etc... A big storm can blow in and change an entire coast line or a slow rise or fall in sea levels can do the same thing. Off the British Isles there is an ongoing project to survey bits of Doggerland to see how people lived there. Here's a very brief article http://www.bbc.com/news/uk-scotland-edinburgh-east-fife-18687504

Is this an overblown hope? Are there projects and technologies being developed that can enclose and drain an area for study?

This is called a cofferdam. They are large and expensive to create and maintain. Typically they can only be used on very small or very important projects and usually only in shallow water. However, on at least one occasion East Carolina University used an underwater cofferdam to temporarily change the flow patterns of the river around a site to keep mud movement down. That was on the Maple Leaf project.

Would such a project be fruitless due to erosion or decay, or would the water preserve better than conditions above?

Depends on the material and the location. Water itself is not capable of fully breaking down wood for example. But there are many critters, bacteria, and other chemicals in water that act on artifacts. In general, cold water is good for preservation because there are fewer bacteria to break down organic materials. This is at Thunderbay on Lake Michigan.

In general, most water is not cold enough for this level of preservation and anything left above the sand is eaten by critters. However, it only takes a few inches of sand to prevent oxygen from penetrating and preventing the bacteria and critters from destroying materials. Buried objects underwater are often extremely well preserved. You might be interested in looking at the Mary Rose Project for some examples.