Some sites require that you accept cookies in order to use them. Does this mean that they can read/track my real IP?

The site I want to use says that it stores permanent cookies on my computer to track various things, for instance if I have two accounts with them. It says "Please note that if you set your browser to disable cookies, you may not be able to access certain parts of the Site for example applying for a job or posting a job. Other parts of the Site may also not work properly." Can I use it with TOR and will it get my real IP because of these persistent cookies?