But it does cause it to drop thereby increasing its angle of attack.
As Paul's sums show, there's already an 11 knot difference between the wingtips without any windshear. That requires some out-of-turn aileron to maintain angle of bank. An extra knot of difference simply increases the out-of-turn aileron required by a small amount, which is probably imperceptible as the extra knot of difference will kick in over the course of 180 degrees of turn. Compared to maintaining control in a moderately gusty wind, the vertical gradient of wind speed is hardly challenging.
The significant issue with low-level downwind turns is in the visual perception of the pilot, as SSD said a couple of pages ago.