I don't think my RSB did anything to my ride height, but maybe I just haven't noticed. Since the rear bar is preloaded when you install it, it is possible for a stiff bar to exert some force on the suspension, but not sure the Cobb is stiff enough for this.
Be aware that changing ride height based off looks may not necessarily offer the best handling, even though most lowering springs main selling point are looks! Some people prefer evenly slammed cars, but depending on shock travel, suspension geometry and corner/cross weight distribution, you could seriously F-up handling. Maybe Mazda wanted the front end a bit higher than the rear for a reason? You never really know until you get the car up on some corner weighting scales.