I have never had any of my doctors suggest the need for a medical id bracelet for this purpose. But when I went to hospital to have my ovaries removed they used a special (bright pink) hospital id band on my surgery arm. This worked well to warn off any staff from using that arm. It was reassuring that I would be ok even when unable to speak up for myself when under anesthetic effects. Would be sensible to think that all hospitals could have this system. But in an unplanned situation (such as an accident or something) it is a worry.
On the other hand, I did come across some information about controversies in lymphoedema that said that there is no actual research showing that taking blood pressure or even blood from the surgery side has ever caused lymphoedema. It went on to say that surgeries on the hand that require tourniquets to be applied by a surgeon have even been done without any adverse lymphoedema reactions. But I know we cannot go by everything we find through dr google!
Lymphoedema is an area that needs far more research so that those of us at risk or who have lymphoedema can receive research backed information and recommendations. Meanwhile we are best to err on the side of caution and follow what is currently recommended by lymphoedema therapists. I think you can actually get those rubber type bands as medical id bands. These are relatively inexpensive and may give you peace of mind.