While I certainly agree with the first sentence, and the second sentence sounds reasonable, Dr. Kirsch writes that healing can occur, even with tears. Perhaps with tears (crying) too! :)
It can also break and then you are up a creek.
Hanging is going to put stress on it and it will probably blow if it is torn badly enough.
And lifting your arm that far can be a problem as well.
After it is repaired or before you tear the tendon, all of the exercises are a real good thing.
But I had a torn tendon, bursa and cuff and went the surgery route and PT after. I now have full use of my arm again.
Doing your full PT and then keeping up the exercises seems to be the key.