If the state was paying and your mother wanted to pay out of pocket nothing would stop her. Elective course of action is not banned in any single payer system that I know of.
Canada -- a Quebec ban on private health insurance was overturned in 2005, but there are still open court cases on whether that applies nationally and whether healthcare providers may charge privately for services.
I don't know about Canada obviously but in Poland hospitals are not allowed to charge for anything that is refunded by the national health service, but they are free to charge for anything else. So if a patient says they want an extra injection that is not funded and they will pay out of their own pocket for it, they absolutely can.
