Does anyone know if a university or department can still reject your PhD application if you are self-funded and your potential supervisor has agreed to supervise you?

Yes, of course they can still reject you. Your application will be decided by the admissions people.

The fact you have a supervisor lined up and you are self-funding does put you in an advantageous position though.

I think it obviously goes in your favour if you have a supervisor who wants to have the topic you are proposing researched and wants you to do it - sometimes it is just a formality - I know it was in my case - but yes, they can still reject you, it isn't down to the supervisor who is accepted or the fact that you are self-funding.