Sports sciences specialist here.
Leaning forwards can help in running, but only when gaining fast acceleration without messing up the posture you'll be in when you straighten out. Since having your arms behind your back automatically means your posture is shite (it also means you lose about a third of the power in your run) there is no point in doing it.
Running like that for more than about twenty metres has no advantage in any circumstances that do not directly require you to have your body below a certain hight and your arms extended straight behind you.
Shall we stop trying to explain this and just put it down to "LOL ANIME?"