I don't think Medicare or Medicaid deny charges if the patient leaves AMA. I could be wrong.
As far as refusing to sign the form that really doesn't matter. What matters as far as the billing goes is the disposition assigned to the patient in the documentation. With most forms of EM documentation there's a spot at the end of the chart to check discharge, admit, AMA, deceased, etc. That dispositon is what matters for billing. Even if a person refuses to sign the form it won't help if you check the AMA box and document that you advised them not to go.