Forgive me if this has been asked and answered. I did not find it in my searchings.

Is it possible to display a message that appears only when a category has no articles, i.e. "This category has no articles at this time?"  Right now on the site I am designing, a category with no articles just displays the Category name and nothing else, so it looks rather barren.

Take a look at category.php Search for numOfItems (root/components/com_k2/templates/default)

Create an override, and edit its category.php and include a test for the variable being 0 and include your message