Did you mean "reduced bank" INCREASES climb rate?
If so, yes it does, as you are taking less energy out of the equation to turn at the "normal" rate.
Think lift vector, induced drag and all the other ATPL groundschool science.
I used to use it frequently on 737 towards ToC as it maintained a better rate of climb whilst conforming to Lateral Nav needs.
Also, if in Hdg mode, passengers awake and looking out the window don't like it when the aircraft rolls to approx 25 AOB at high altitude, it makes them think "here we go, we're all going to die!".
If using this feature, remember to reset normal bank angle to avoid embarrassment later in the descent/approach.
