i think you wanted to say "toward" my fitness.
And no - I wouldn't think there would be any positive benefits. First, let's consider that this is actually possible for humor sake. Second, realize what your endocrine system will do when you crash down later. You will be so zonked, your metabolism will probably slow down, and you won't be able to mentally get through a workout. You would have wasted all that caffeine (which would have been perfect for a long run), and made yourself weaker.
But I think you should try it. Strap on a heart rate monitor and start drinking. Hit laps splits every 5 min and graph your heart rate later. Post it here.