I know it is your quilt and you can do whatever you want. However......
If I were teaching someone to quilt I would not start with a rag quilt. I would use the fabric to make a more traditional quilt ..top, batting and back.
Rag quilts should fray on the edges. That is why a more loosely woven fabric is used.. That is not to say the scrubs would not work. I would put the scrubs in the middle or one the back if you are using only two layers.
I always say you have to respect the nature of the fabric if you mix different fibers, weave, textures and weights. I believe you need to experiment to make sure if you are getting the look you want.
It appears also based on how you have described your student that you need to consider what she wants and avoid making something she may never use.