fruitbatflyer,
I`ve never heard of that procedure! If it`s not written, don`t do it! To spare engine time, VMCs, etc..., has you said, you already have the reduced thrust takeoff with the assumed temperature.
Improoved climb is always a last resorce when 2nd segment climb limited, but long runway available! It is also wise to use improoved climb with the next flap setting when windshear has been reported. Also improoved climb reduces tyre life!
Cheers