MY INTERPRETATION OF THE QUESTION [NEW]
Here is an image from GlobalSecurity.org which I have modified to illustrate my interpretation of the question. The angle of attack of the wing is exaggerated in the original image.
My interpretation is that the question involves only vertical movement of the wing - e.g. along the vertical red lines from the lower image to the higher image. The question noted that "the thrust vector is always horizontal". And, as the image above shows, the direction of the relative wind in relation to the wing does not change when the wing moves up and down.
MY CONCLUSIONS
Yes, I believe that you could make the wing move up the pole. You would have to make sure that the wing has a positive angle of attack (AoA) since that is required to generate positive Lift. The AoA can be created by the shape of the wing or by tilting the wing back. And the engine would have to be able to push the cart fast enough to use that AoA to generate the Lift necessary overcome the Weight of the wing.
However, I am limiting my response to the exact question you posed in the body of your discussion.
ADDITIONAL NOTE [NEW]
One problem with the vehicle design in the example is that it will be hard to stop the wing from flying off or hitting the top of the beam. Once the vehicle reaches the speed required to cause the wing to generate excess lift nd maintains that speed, there is nothing to stop the wing from continuing to rise. But I don't believe that is a problem because the purpose of the question was only to determine whether the wing would start to rise vertically.