Well as far as my own opinion, I think it would be fine pulled back.
When I was in nursing school
, dreadlocks were a big no-no, no matter how clean they were or if they were pulled back. I had wanted dreads for a long time, but knew it wouldn't fly in nursing school. Also, I live in the western part of N.C. In other areas they may be a little more lax.
My friend actually dropped out of the program because they told her that either her hair could go(she has had dreads for years) or she could go.
However, I have since graduated nursing school and have had dreads for months. My hospital policy states that hair is to be clean and pulled back, and that's what I do.
I would just ask. I did at work, and they were fine with it.