I am a firefighter/paramedic, so I'll answer that for you. I cant say that I have ever looked or saw anyone look at a pt's phone for this info. Not for what I think you guys are talking about anyways, which I assume would be some sort of tramatic injury leaving you unable to communicate. We have made a bunch of calls for an elderly person living alone, looking for a person who makes medical decisions, or could convince them to go to the hospital, ect.
The bracelete looks nice, and I am sure we'd notice something like that assuming your arm was still attached . We look for the med alert braceletes worn typically by diabetics, so even a dumb fireman might find that.
The hospital starts digging in pockets a lot more than we do looking for that kind of stuff. They usually start with the wallet (prob looking for ins info) so thats where I would keep something like this...