Dumb thought,

but I tend to wonder about stuff with no need to know, so don't anyone tell me the answer has no purpose.
Assume, (yeah I know), my POI is perfectly centered on target and crosshairs are on the exact center of the scope adjustment knobs. What would the hole pattern in the target be if I rotated the gun through all 12 positions of clock hands? Let's say 40 yds. with 2" maximum trajectory height. Thanks in advance if any one answers this.
 
The pattern of holes would be that of an ellipse, not a circle.

I'll post a diagram shortly on why that is. 

Here is the diagram. The line of sight is the Blue line, while the trajectory is Green. The Magenta line shows the line of the bore. This shows what the rotation does with respect to the line of sight. If the gun were to be rotated about the barrel axis, the scope would move in a circle, but the trajectory would still be constant. 

viewFile.html
 
If you rotate the rifle all the way around, and the scope from 12 to six o'clock, the pellet will drop drastically. The pellet will cross the sightline as usual, but in a oposit direction- down - and down it goes all the way. No trajectory arc between the sightline, just the pellet crossing on its way down. There will be a huge under-poi so to say at 40 yds. Canting right will throw the pellet to the right, and a lower impact since the top of the arc will be reduced accordingly to the canting. 
Edit: Irons post crossed mine, but his diagram explains it all.
 
"Sprocket"....What would the hole pattern in the target be if I rotated the gun through all 12 positions of clock hands? Let's say 40 yds. with 2" maximum trajectory height. Thanks in advance if any one answers this.
This elegant interactive answer to your question is the work of the talented (!!!)Mr. Perry Babin.




http://www.arld1.com/images/swfs/targetplottrajectory3.swf
 
So I was half right lol. It does make a circle just not around the poa but bellow it. I never gave much thought to how it would impact while holding upside down. I knew right to left cant would throw the shot to either side. After reading Gunnertrones statement about shooting upside down and using the target plotter from Steves link it makes sense why it would be below the target.