ZZP did a bench test ith one of their IC set-ups.
Without changing anything (timing, pulley, etc.) they pulled a few ponyies just from adding the IC. IIRC it was like 5 hp.
So you're both right.
ICs support things like smaller pullies and increased timing by cooling the charge temps, but at the same time, because the charge is being cooled and condensed, there is a little more power from the IC alone.