Yes. They’re well within their rights to prevent you using their own equipment and connectivity for personal use, be it personal email, online shopping, or using social networking sites.
Some employers will be happy for you to use it on your clearly defined breaks during the working day. Others who want to structure work in more flexible ways will be happy for you to take occasional breaks when you wish, so long as you make up the time overall. It depends on the management style of your employer.
This also covers use of a work email address to register with the service, as it is provided by your employer. Even if you only use it at home, you need to know that you're permitted to use the email address in this context. In any case unless you are using Facebook officially as part of your job, it would be better always to use a private e-mail address, rather than your work one.
