Would a airfoil move backwards if you rotate it vertical
A practical example of your question is when a model aerobatic aircraft with a conventional aerofoil profile (ie, not symmetrical) is fitted with a sufficiently powerful motor that it can be made to hover in the vertical position. This is quite a common trick. 

The answer is yes, there is a force in the direction of the red arrow.

The model might drift in that direction, although there are other aerodynamic forces, torque, centre of gravity &amp; thrust vector issues that will affect the balance, and these will change as power is increased and the model goes from hover mode to vertical flight mode.