You will never be refused emergency treatment just because your insurance 
   doesn't cover it. That's the law in the United States.
   You will get a huge bill afterwards and there will absolutely be financial 
   consequences, but not medical ones.

Even ignoring the financial consequences, you literally have no idea what you're talking about. Hospitals are required to patch you up this second, yes -- but they don't have to treat underlying conditions until you're going to die from them. Regardless of how much damage that does. You can certainly die of very treatable diseases. Need a ct/mri, blood scans, cancer tests? Well, unless you're going to die of it this second, a hospital is not (and often won't) required to perform them.

The law you're citing -- EMTALA -- merely requires hospitals to stabilize patients.