It doesn't work. I have tried sprint jumping as you suggest and he simply won't grab the ladder on the other side.
I have died about 200 times trying to jump this gap now. My buddy came over and he tried like 30-50 times too. I don't know if since some people have managed to make it across with no problem, if it's because of a platform difference, or if there is a bug that happens with certain graphics cards, but it really does not work.
There are a ton of people having the same issue so I know it's not just me.
Here is just one example: http://battlelog.battlefield.com/bf3/forum/threadview/2955065670120893181/