Wi-Fi yes, Cellular no
I just traded in my 2013 Model S for a 2016 Model S and although there was no difficulty, other than slow to load I was able to connect iPhone 5 and then iPhone 6s with the 2013. Now, only on Wi-Fi connects to the app and the car. Cellular "cannot connect" Tesla Support had not heard of or could offer a solution.
Orlando_Jack about
Tesla, v2.7.8