I think the problem with this theory is that if you're going to give everyone life-saving emergency care, you might as well give everyone ALL care, because it's a heck of a lot cheaper.
For instance, someone who is poor has strep throat. Strep throat, if left untreated, can develop into rheumatic fever, which can cause heart failure and death. For the price of four dollars in penicillin, the strep throat could have been treated, but now we--as taxpayers--are stuck treating a patient who could have heart failure, which is a much more costly scenario.
I'm not saying that we should treat everyone. In fact, I don't think health care is a right at all; if you can't pay, you shouldn't get treatment. That said, if you're going to treat emergency cases, seems to me like it's a lot cheaper in the long run to treat everyone universally.
Yes and no. One of the big problems with a lot of the uninsured and Medicaid-type patients is noncompliance. Some is understandable (lack of reliable transportation to whatever facilities), some ignorance/inability to understand complex directions, and some just downright laziness.
I'm sure there are statistics somewhere, but the failure rate (patients who don't show for appointments) is huge for those getting the care for "free."
Emergency rooms and hospitals are an expensive way to treat people. Many areas of the country have low cost clinics. I'd prefer to subsidize the low cost clinics than to treat people in expensive facilities. The co-pays in the clinics are usually low so that people who need treatment for minor illnesses can get it, but it's not free, so people who have flu aren't tempted to seek medical care.
Anything short of making people responsible for their own health is going to be too expensive.