It does not appear this is possible through the standard TFS alerts setup. The main issue is that the status of the test case (active, passed, failed) is actually associated with a test run and not the test case itself. The test run does not appear to be a work item I can query against.
I believe we will go with creating a bug when a Test Case fails (easy enough to trigger emails regarding new bugs)...I think this maybe the more "traditional" approach in the Scrum template.