even a 1/4" vertical rise increases torque slightly, but the longer the increase in length, the more the torque increases.
on your crow foot theory you are correct, and that is also how the torque extensions work, because they aren't perfectly centered, the offset between the ratchet head and the socket is such that the length cancels out the mechanical advantage. also in a perfect world, a vertical length would offer no advantage, but due to human error, the extension acts like a lever, even though you think its perpendicular to the fastener you are working with.
I used to doubt this myself until one of my buddies showed me a trick. I was working on a project struggling to get a rusted #24 screw out of a flat panel. I had plenty of room all around the screw, literally miles. I was using a typical #2 cross tip screw driver to get the suborn screw out with out any luck. My buddy came by and saw me struggling. He said "Why don't you grab a longer screw driver?"
I got into an argument saying that a longer screw driver wouldn't help me, yada yada, yada. But I finally gave in to shut him up... But to my surprise the longer screw driver he handed me did the trick. I had been using a #2 Cross tip with a typical 6" shaft and handle. He handed me a 24" #2 cross tip, and it worked like a charm. After words to prove his point on how it worked, he took out a 1/4" drive torque wrench, several extensions ranging from 3/8" up to 24" and a didgital torque scale (used for calibrating torque wrenches). We set the Torque wrench to 5 lbs and hooked connected it directly to the scale. When the Torque Wrench clicked and wouldn't let any more torque be applied to the scale, the scale read 5 lbs/ft. We torqued three more times to give us an average for comparison. each time the scale read 5 lbs/ft, so we then added the shortest extention and the scale then read 5.10 lbs/ft... (at 5.05 lbs/ft we had to send our torque wrenches off for a replacement) and each extension we used there after kept climbing... at 24" we were pushing 18 lbs/ft.