Is there a way to disable the "Visible By Administrators Only" message that appears when a page is viewable only by administrators and the red box that surrounds each control on that page?

Yes...

Always assign a page to be visible to at least one role in addition to Administrators, even if no-one has that role. Create a role just for the purpose.

or, if you just want the borders gone and the message left behind, add this to your portal.css:

.DNNAlignleft,.DNNAlignright,.DNNAligncenter{border:none !important}

Rob

Udated: And I guess you could remove the message in the language editor but I'd keep it there for a small reminder.