If you JB it (if you can?) and are running CFW then you will NOT be able to go on PSN.
If you JB it and use a hardware kit such as E3 Flasher or Progskeet then you could dual boot which is having CFW and OFW on the same console (sort of lol), but you cannot have OFW and CFW at the same time so you could only use PSN when running the OFW side of it and with that OFW you can NOT have any homebrew at all, and that includes running backup managers.
Hope that covers the main points for you?