I've tried checking and unchecking this box and neither seems to remove the messaging settings from the student's profile. To turn it off, I assume that you check the box which is the opposite of the default setting. 
Students till have the 'message' settings show up as an editable item in their profile.
Debbie,
I apologize for my delayed response, I have been looking into this and I the only solution I could come up with is a CSS Hack
#settingsnav .block_tree li ul li:nth-child(3)
{
display: none;
}
Important: In my testing this will remove the messaging option for students, but for other roles/users it may remove a different option.
The code looks for the third item in the settings nav/block and hides the 3rd one down.
For example, with this CSS installed it would hide the "Roles" option for admins.
Now.. as an Admin myself I must say I don't use that link very often but I felt I must fully disclose and warn about a potential side effect.
This code can be placed in the custom CSS section of your theme in the theme settings, if your theme does not have an option there, you will have to add it to the css files for your theme on the server. I tested this on the afterburner theme in Moodle 2.5
I hope this is useful.
Thanks
Chris
Thank you!!