We don't know if mobile app access is included with the car or if you have to have a connectivity plan. I assume that even if you don't buy the plan that Tesla will still have a connection to the car to pull logs and do software updates but we don't know if they'll let you use that channel for the app to control the car or not.
I would guess they would since if you chose to use tethering for the car's connection then once you left the car the app wouldn't work but we haven't explicitly been told this.