As a mother of a teen, I'd say probably not. A dozen teens is a lot, and even if you're basically good kids, you get that many together and common sense seems to go out the window. Also, even if the house is already rented for you, I've been to a number of beach houses in that area and many stipulate that there must be an adult in the house. If you violate the rules of the lease, you could conceivably be kicked out.
I have to agree with Sari here - I don't care how responsible teens are, but you get a bunch together, and something may, and most often does happen. I am an uncle myself, and if I was responsible for my nieces or nephews, I would insist on having at least ONE adult on the premisis at ALL times, because then you would have someone available if someone gets hurt or has a medical emergency. If that happens, an adult can help you and get the help that you need.
I am not saying that adults have to "hover over you", but at least ONE should be available to you in an emergency. This is equally important if you or your friends have medical issues, or if you are swimming or you have something happen IN the beachhouse or ON the property. As Sari says, the lease may say that there must be an adult in the house, and if violated, you could be kicked out.
Without an adult on site, I would also say no.