I'm not really sure what your question is.
Throw an arrow behind you? well her turn rate was buffed to 900 to get those nice spears and leaps.
Not sure if that answers it though..
If you mean during Leap, no because you can't perform any action while you're bounded to its projectile.
It was "possible" to do this in DotA during Leap, but the chances of pulling it off successfully were very slim.
If you mean if it's possible to cast an arrow behind Valkyrie without actually turning, no.