and what effect it could have upon them when suddenly unexpectedly buzzing and vibrating
It's rare that I fly an airplane so smooth that I could feel the phone vibrating in my pocket! In any case, the pilot should prevent it being a distraction during flight. However, I find value in it being available in the case of emergency. I admit, that a couple of times, I have used it to pull up internet weather radar, when I needed up to date storm tracking. BUT, at the student pilot level, the student should not be needing to do this, and the instructor should not be tinkering on the phone during a lesson either - unless to assure flight safety.
I like the idea of having a cell phone available in the case of a crash. Toward this end, I put my cell phone in a waterproof bag, and clip it to my life jacket when I water fly. Unfortunately, two years ago, when my student sent me out of the plane through the windshield, and into the water, the phone bag, as well as the bottom edge of my inflatable lifejacket, were torn off on the way past the windshield. My phone was never found. My wife called it for a couple of days, and eventually it either flooded, or the battery went flat, 'cause it stopped ringing. It's down there somewhere. The only things right about that accident were that we both lived, and my student crashed in front of people with boats, rather than the middle of the lake.
Take the phone, but ignore having it unless everything has gone wrong....