Does the member see the order comments box?

No.  This is an internal section, for you to put notes relating to the order.  The member can't add comments, or see what you have inserted in the comments box. 

To add a comment on an order, go to the order page in the admin panel.  Scroll down to the comments section at the bottom of the order.  Add your comment and then click on the Update button.

 

Order Comments - click to enlarge