Yes. Your employer would be well within its rights to prevent you using its computer equipment and connectivity for personal use, be it sending personal emails, shopping online or using social media sites.
Some employers will be happy for you to make personal use of the internet during clearly defined periods, such as breaks or after hours. Others who want to structure work in more flexible ways may 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.
It may also be relevant to consider whether your employer permits you to use a work email address to register for social media services. Unless you are using Facebook officially as part of your job, it would be more appropriate to use a private email address.
In any event, the rules (and the likely punishment if rules are broken) must be clear, and they must be well-publicised so that everyone knows what they are.
