I have 2 (for when I lose the first) and when I was in hospital in November, they were brilliant. I am not sure how well the anaesthetist would have responded if I had just told her about my missing nodes (before she put me under, obviously), but having the band on made it look "official" (even thought it only cost a few pounds on the internet) and she was very agreeable to do her best to only stick needles in my non-affected arm, even though the veins on my affected arm look so much more tempting.
We did agree that in case of emergency, she could do what she felt necessary (needles in arm, knock out the bridge on my teeth etc), but it all went smoothly after the inital challenge of getting a canula in.
The nurses all respected it too when taking my blood pressure.