Sorry to say it, but in an "Emergency", the last thing they're gonna worry about is that ring. Your finger can sustain quite a bit of damage and survive anyway. I am sure that they would submerge your finger in ice to limit the swelling, probably shoot it up with some novocaine and get to work removing it, but it would be removed. Decreased blood flow to your finger is hardly life threatening or requires dire attention, even in an emergency. I think you're far too concerned with this.
