There's no yes or no answer to a question like that. It depends on what a hypothetical universal health care system is set up to cover. That varies from country to country.
In Canada, If a person qualifies for a health card*, he gets treatment. Just like smokers, drinkers, skiers, skydivers, mountain climbers, etc.
*Citizens and Permanent Residents. Others, like refugees, I'm not sure about, but I think so. If you are here illegally, you don't qualify. If you turn up at an ER with blood pouring out of you, you'll be treated, certainly. Of course, all health care systems will have inadequacies. But, complaints about illegal immigrants costing taxpayers excessive sums of money is not one of them.
Sure it will. I understand that most medical research takes place in the US and, until recently, the vast majority has been government funded.
How would I develop a plan and who would be covered? It's not for me to answer - that's up to you guys. And low income people here don't pay income taxes either. Doesn't matter, they're still covered.