Can you damage a bravo XR drive coupler or U-joint by starting it (rare moment of confusion and no power transmitted) with the trim all off the way up? I had heard that limit sleeves provide some protection in the XR. Any one know for sure.

Yep,you Can Hurt The U-joint And Coulper In Any Bravo Drive Running It With The Drive Up.even In Neautral The U-joint Turns.

I understand that, however I was looking for some input on whether the trim limit sleeves in the trim cylinders provide protection for the beefier u-joints and input shaft in the XR.

The trim extension is limited from 27 1/16 to 26 7/16 inches to protect the U-joints. See merc bulletin no 2000-8.
Tilt limit kit part # 15768A3.