Yes, it's a good idea.
BUT there's a couple of issues with just having ICE information on your phone...
As one lady mentioned on our Facebook page, she'd been involved in a smash and no-one could find her phone, when she got out of hospital she did find it- a few days later when she went through the wreckage of her car.
Mobile phones get smashed, their batteries go flat and people lock their screens so it can make matters far more complicated. Now don't get me wrong here, I have ICE info on my phone too, but the little red USB key stands out within my keys in the ignition of my car and my motorbike. By standing out, it gives emergency responders a very visual clue as to what it is.
The term ICE- In Case Emergency is an internationally recognised term to emergency responders.
I'm not saying have either/or, I advocate that you have both.