Cosmetic surgeries continue through Covid

Even though the health system is hurting, doctors, nurses and other medical professionals are still performing cosmetic surgeries.

Supposing someone books in for a serious cosmetic procedure, and it goes badly. They crash and have to be resuscitated, they need more extensive support than a private cosmetic facility can offer, so they have to be taken to a regular hospital. Do they get this for free on the public system, given that they undertook the risk voluntarily and not out of medical need?