No they don't.  These tests are assuming LMS (which also has external_auth as an INSTALLED_APP), mainly b/c they use the LMS URL schema.  They don't run under CMS because external_auth is not an INSTALLED_APP.

Actually the implicit assumption is that SHIB is only used on the LMS side, even though it's in common, again because the login/reg handler functions in external_auth/views.py assume redirects to LMS student views.  
I should put a comment somewhere. Probably in envs/common.py for both LMS and CMS.

Actually a broader question.  Should external_auth be in common anymore?  I can see student being in common for the models, even though the views are all LMS specific, but I don't know if the same can be said for external_auth.