Will the thick side of the hinge pull the tree in that direction? NO! the face cut will determine the direction of the fall, as long as the hinge doesn't fail. However if the tree has side lean, and the hinge brakes, the tree will fall with the lean. This is why you make the hinge thicker opposite of the lean, this makes the henge stronger preventing it from failing too early in the fall. So as long as the tree represented by the OP has no side lean, the tree will fall in the direction the face was gunned.
The offset thick hinge DOES NOT pull the tree to one side. The hinge is for support, the face determines the fall.