I do not think that the inability of Tesla's smartphone app to connect to the car is related to the ability of the car to display Supercharger station status. The app does not display Supercharger status.I saw early this morning 2 supercharger locations as completely full. VERY unlikely
Currently my Tesla app on my iPhone cannot connect to my car. On the other hand, my car nav display shows information the Supercharger stall status of all the Superchargers in my area. They appear to be about the same level of occupancy as usual.