No, you can have surgery as a self-funded patient. You will have additional costs for the hospital including theatre and bed fees that the health fund usually covers.
Though unlikely, if a self-funding patient has a complication from surgery and requires re-operation, ICU or extended length of stay they may require transfer to a Public Hospital for financial reasons.
It is preferable that patients have private health insurance, though there is a 12-month waiting period after joining to allow access to this. The larger cost for the operation is not the surgeon fees, but the Hospital Fees. We advise that patients check specifically that their health insurance policy includes obesity surgery (e.g. item numbers 31572, 31575).