Tested on Moodle 2.2.3, 2.2.5, 2.3.2
Moodle 2.1 was reported to be OK
Forum : https://moodle.org/mod/forum/discuss.php?d=213846

Scenario:

• Course #1 has materials (any resources or activities) and quizzes. Questions for quizzes are stored in the context of Course Category #1
• Course #2 is located in another Course Category #2

If you try to Import content from course 1 to course 2 via Course Administration > Import link, then nothing will get transferred. You will be presented with "Import complete. Click continue to return to the course."
But course 2 would be empty, and nothing will get transferred.

One has to exclude quizzes during Import - only then the rest of the materials can be imported.

If, however, you will Backup Course 1 and Restore to the Course Category 2, then it will "work".
You will get the message "The questions category "Category 1", originally at system/course category context in backup file, will be created at course context by restore".
So Moodle will create a new COURSE-level question category titled "Category 1" and put a COPY of the question there.

Other users reported that Moodle 2.1 did not have such issue.

Related post with more testing results: https://moodle.org/mod/forum/discuss.php?d=226382#p993391