That it does not. Best the app can do is leave a message in the notification area. This has been an issue for me as the app is silenced with the quiet time I have set in Cortana. I have to have the admin for our group add me as an SMS contact, too so I can set Active911 in my circle of friends to break through during quiet hours at night. It would be cool if apps could also be included in the circle inside Cortana.
Good luck with your search.