It's an interesting idea, but I'm afraid it's not currently possible to do this via the admin interface. But, you can do this via a minor code modification - in qa-page-ask.php, find this line:
$categoryoptions=qa_category_options($qa_db, $categories);
After that line, insert something like:
if ($qa_login_userid!=USER_ID_OF_SPECIAL_USER)
unset($categoryoptions[CATEGORY_ID_OF_SPECIAL_CATEGORY]);
Replacing the capitalized phrases as appropriate, of course.
To complete this, you need to do the same thing in qa_page_q_edit_form() in qa-page-question-post.php, so most people also can't use the special category when editing their post. You'll also need to add $qa_login_userid to the list of global variables at the top of that function.