In a paper of Heier and Wong, It is written that from a pointwise argument due to Berger does follow that the scalar curvature (and thus also the total scalar curvature) of a Kaehler metric of positive holomorphic sectional curvature is also positive. I am looking for the paper of Berger ("Sur les varietέs d'Einstein compactes, C.R. IIIe Reunion Math. Expression latine, Namur (1965) 35-55") to which Heier is referring, but I don't have access to Berger's paper so I ask here to see if this can be proved very quickly or has been written in somewhere else.
The answer to your question is exactly the same of the answer to this older question of mine. Enjoy!