Yes, but what sort of health care? Real care often gets withheld from ME/CFS patients by national systems, which is where it can be beneficial to be able to afford to go private.
I don't know of any specific healthcare for ME/CFS. I'd love to be wrong on this, that's why I'm here, looking.
[So although I am not in any way being treated for ME/CFS I did get simple things like melatonin to trial for sleep (I take only on specific nights when I know I'm crashing) and more regular doctor's visits and blood tests to keep an eye out for standard markers. My doctor has no treatment for ME/CFS. The only treatment I know of is rest and self regulated pacing. I live in a remote, quiet location and eat a balanced diet similar to what my grandmothers (who were long lived healthy) did. I try to keep up my social contact while reducing my exertions.]
My doctor's job is to make sure I'm not suffering from other problems that can be ameliorated.
[My job is to live a tiny, puttering, life in my prime and not go mad.]
Living in a country where evidence is required (and weighed against the strength of evidence and benefit for treatment of other medical conditions) before resources can be committed has been hard, but it has saved me from wasting too much of my limited functional time and energy on pursuing personal remedies when the real need is for shared investigation and replicated research.
[I sometimes wish my doctor gave me remedies, it would help me feel like I'm doing something to fight this thing. But really what I need is to know that they are listening and analysing what I'm telling them, combing through it for anything they can investigate further or treat. There are tests people in the US all seem to take like MRI with contrast on the brain to look for lesions etc. but here I can't get (except perhaps privately). Why? Because until the symptoms are even worse, the treatment for anything it could be is not yet indicated. I very seriously considered getting much worse in order to get a firmer diagnosis. Then I read the stories of those who have and are still without treatment. I realised that, ironically, most 'treatment' for ME/CFS is for the psychological benefit of feeling validated. Until we actually have research that identifies what is going on, who has what, and what we can and can't do about it, it's up to me to find non-medical ways to cope, to recognise the reality of my condition and treat it seriously, without medications, tests or treatments that are not yet indicated.]
If I have anything that medically indicated treatment, which research confirms is more likely to help than not, I would get it through the public health. Or I would be able to lobby for it. Or join a university trial for it. Etc.
Edits: just extra spacing for readability. I'm sorry this is long and probably OT so I won't keep going into this one here.
I'm not suggesting public health is always great, just that having your basic needs met is a factor in severity of illness.