almost there
well, yes, carb heat reduces power developed--for a given throttle/collective position.
But it's not that you then have to pull more power, for the airframe itself doesn't see the carb heat, it just needs the same amount of power to beat the air into submission as it did in the first place.
So you have to increase the THROTTLE ("pull power") in order to open it farther and let more, but thinner, heated, combustion air into the engine, in order to produce the SAME power as pre-carb heat.
Throttle open farther will reduce suction in intake manifold, so the MP will show a higher number. Lots higher, most of us "discover" we forgot the carb heat was on when we flinch at the outrageously red-lined MP.
Now, ONWARD! To the methodologies of splitting hairs with only an Exacto knife and a hand lens . . .