I've seen this twice in my life outside of training. Both instructors.
First case: I was joining the local dive shops in one of their recreational outings. The leader of the dive was the shop owner (Nikos -
@wetb4igetinthewater knows him). One of his double tanks was leaking some gas from the neck. Not a big deal but as I was relatively new diver I considered it right to let him know, so I signaled to him small leak and pointed to his manifold. He remained very calm and withing seconds he had his BPW with doubles straight in front of him, saw the leak replied to me that it's ok and put it back! All this while maintaining perfect horizontal trim and keep (slowly) fining/moving with the group!!!
The way he did it was to unstrap his weist strap and then pull with both hands the manifold on top of his head to bring his rig in front of him. To don it, he put his hands through the shoulder straps with his rig in front of him and then pushed his BPW/tanks back on top of his head.
Both him and his BPW/tanks seemed to be perfectly trimmed and neutral even when separated so he could effortlessly hold his rig in front of him. It looked like he could comfortably do the whole dive like that.
Second case. Towards the end of a dive during an Egyptian LOB we were slowly fining at SS depth to reach our boat. Out of the blue the dive leader removed her BCD/tank, had a look at the back/side of it for something (no idea what she was looking for) and put it back like nothing happened. Again she remained trimmed and neutral throughtout.
The way she did it was to remove on hand from the shoulder strap and rotate her rig around her other hand in front of her, saw what she wanted to see, and reverse to put it back.
Both dives were in calm. clear, warm water.
Since I dive solo frequently I have tried to practice this a couple of times. Yes I can do it, but not nicely.