Last year I brought my laptop to school to take notes on. As someone with terrible handwriting, it was was enormously helpful. I will admit, though, that I did not hesitate to browse the web during class. Sure, the school put up filters, but HotSpot shield (and in my case, an SSH tunnel) could circumvent them with no trouble. A few students spent all of their time on sports websites, only getting minimal notes for the purpose of plausible deniability.
So your old high school should know that it is impossible to block students from messing around. However, laptops can be very useful. At my sisters' schools where laptops are required, teachers are using tools such as Moodle for homework, and email for communication. These make it more convenient for everyone. Whether the latter balances out the former is difficult to judge.
If one wants to learn one will use his laptop in this sense, for a serious student using a laptop can boost his performance. If one is not interested in learning,one will find other ways to distribute his attention.
What your school should not do is to impose regulations about the operating system and configuration a student laptop should have. A student should have the liberty to run Windows, Linux or Mac on his computer. A diversity of machines will let others to learn about alternatives. They should be encouraged to learn to use as many applications as possible.
Today, the education should not be about quantity, but about creating the mind set for organizing the information. About learning to think with your own mind. In this sense a laptop could be a valuable asset for letting the students access this information.
Requiring laptops is like requiring paper. You just don't need to do it.
A requirement for laptops should be in response to a specific educational purpose. Sounds a bit like the tail wagging the dog...or free laptops for administrators for every 50 the school buys. Curriculum should come first, not technology.
They won't pay attention to the teacher for sure. If there's a web filter then students will download games from home and put them on; especially Flash games. If even one student knows they can do that, then it'll spread pretty fast... And I'm sure there will be a good handful that do.
I think basically, if you give students something to do other than listen to their teachers, most will stop listening.
It's better to let students bring laptops, so the serious ones will actually put them to use. Maybe they could even make laptops available to loan, if poorer students want one but couldn't get their own?