if you leave the shell on the shrimp when cooking, will they stay large?

If they aren't overcooked they will stay the same. Most of the time if you buy them they will be precooked (pink) and more cooking will make them shrink more.

You then have the hassle of shelling them, either on the plate or prior to serving as the rest of the meal will get cold. It is quite a knack to shell them and if you have guests they would probable need to be shown

Dune

No, it might keep them from curling a little. Most people over cook shrimp. Many cooking shows say they shouldn't encounter high heat at all.If sauteing, it shouldn't be above 140 -150 degrees, which would be like medium heat on a burner, and only for about 2 minutes or so. They will be much more tender, have better flavor, and won't shrink so much. In boiling water, you shouldn't need more than a minute or so. They also continue to cook after you have taken them out of a pot or pan. The shells will add flavor, they make shrimp butter out of sauteing the shells in butter to extract the essence. Don't forget to de-vein them, if you didn't do it before (actually they will be safe, but most people are opposed to eating shrimp intestines).

If you overcooked the shrimp whether you boiled, grilled, steamed or deep fried, the shell will shrivel and the meat will shrink. Just don't overcooked the shrimp. Make sure the shrimp turns pinkish and when you gently press on the shrimp, there is a resilient (elasticity), its good to dish out.