There are a multitude of ways to measure the length of a shot string. They're just not easy or convenient for regular folks who don't have a lot of sophisticated laboratory equipment available to them. I suspect high speed, high resolution, time-lapse photography would be the most likely candidate for getting the answer.
I applaud Pat's efforts in trying to chase this ghost, but in the end, other than just "because I wanted to know," what has it told you?
It can't buy you a target, in my opinion. Those who say it can get you one if the target flies into the side of the pattern? I think that's wishful thinking, or lack of a grasp on the facts.
In answer to the original post, gun fit is far more important than either shot string or pattern, though pattern is an important factor. But as hmb said, shot string and pattern are both irrelevant if the gun doesn't shoot where you are looking. And that's the bottom line.
And I tend to agree with what Neil said, that a short shot string is better than along one. But how do you know? Well, you don't. And how do you test it? Well, that's not easy. And in the end, what is it worth? Not much.
Mathematically, at an angle of incidence of 25° (assuming zzt's geometry is correct, between the trajectory of the target and the trajectory of the shot, but I think its even less than that angle), even if we assume the target is still traveling 42 fps (it won't be, it'll be moving much slower than that) and we assume the shot has slowed down to 900 fps, and we assume a 12 foot shot string (which, frankly, is anybody's guess) between the time the very first pellet in the pattern passes the target and the very last pellet passes the target, the target moves only about 4" towards the pattern. If you didn't hit it with the front of the pattern, and it only moves 4" into the pattern, you aren't going to hit it with the back of the pattern.