At a Zero AOA a truely symetrical airfoil creates Zero lift. Simple aerodynamic physics. A symetrical airfoil MUST have a Positive AOA (relative to gravity) to create lift. Will a plane with a symetrical airfoil climb without a positive AOA? Sure, if you have enough power/thrust. But the wing still won't be generating lift.

As for Hossfly's comments on "what a pilot can control". He can also, in some cases, control the airfoil shape to change the amount of lift/drag generated. This could be done with leading edge devices(slats,etc) or trailing edge devices (flaps).