It will cause a very temporary increase, but as the chlorine is broken down by stuff in the water, the byproducts negate the higher pH, so as an end result it shouldn't change.

If you have any aeration (a heavy rain that bubbles at the surface, or splashing kids in the water, would do it) in the pool, or a SWCG, those are common culprits for rising pH, as well as higher pH in fill water.

Janet