How long does it take for the Sharpshooter to eject one shot?
Well, the above 3 captures are one frame apart at 30 frames per second,
(1/30 x 2 = 0.066 seconds)
so based on the above 3 frames it could safely be said that the sharpshooter forms and ejects its P-wad in less than 5 hundreths of a second (< 0.05 sec.)
So, if this guy had enough "ammunition" he's be good for 20 shots a second which would beat out the vast majority of machine guns,
but he'd still easily be outgunned by the gattling gun on a Black Hawk which is good for 90 shots per second.

Click on the following link to see a sharpshooter in action!
Note: Don't forget to hit the little geary thing and set the quailty to 1080 HD.
Viewing full screen will also allow a better look at his "gun"
in the cropped detail of the last 30 seconds.