If I'm flying in Sport Mode, and I lose connection to my controller, and failsafe RTH is engaged- will the Mavic switch back to P-mode? (I'm worried the forward obstacle avoidance might be disabled in this situation…)

only one way to find out, have it close enough to you and turn the controller off then check the flight log and see if it did or not

It should automatically switch back to P mode for RTH, assuming it's possible (enough satellites etc.).

This iscovered in the user guide ...

You can find it here

http://www.dji.com/mavic/info#downloads

It has a whole lot more detail in it than the one that comes the the box

It comes back quicker!

If forward vision system is enabled and the lighting conditions are sufficient, it will avoid obstacles when fail safe RTH is engaged even if you were flying in Sport mode.

DJI Mindy Posted at 2017-1-2 23:09
If forward vision system is enabled and the lighting conditions are sufficient, it will avoid obstacles when fail safe RTH is engaged even if you were flying in Sport mode.

Why does my Forward vision system shut off when I click on RTH?