The computer that you are on has an ip address that will be stored on the isp's server when you dial in, but you will then be issued an dynamic ip address that will be different than the one you are using,you also may be going through a proxy server at work which will also give you a different ip, but just to let you know you can be traced because all ip's are logged, BUT it would take alot of work to trace you depending on firewalls and such, if you aren't doing any hacking then you should be ok.
If you are just going to send somebody a big fuck you from page net,then you will also be ok,but i wouldn't go too far with it.