No if the wind changed direction the plane would speed up at the same rate that the wind was changing in speed, have you ever seen a leaf blowing in a wind which keeps changing speed?
The plane wouldn't suddenly speed up. What's keeping it in the air is the air passing over its wings, which is just enough to keep it in the air. If you look at its angle of attack, it's pitched quite high but not gaining altitude, meaning he's right at the thresh hold for a stall if he loses any more speed (The head wind slows down, or changes direction) It will fall. He has no altitude to gain any forward momentum in the case of the wind changing direction
Ever heard of Wind shear? It's basically that, that I'm referring to. Horizontal Wind Shear