FFF
I don't believe your explanation is correct (but I don't know for sure)
The normal operation of a carb (or a fuel metering unit) is that it measures the flow of air (actually it measures a parameter which is a combination of volume and mass flow) and dispenses the fuel accordingly.
So if you reduce the airflow, the fuel flow must also reduce. But do you actually reduce the airflow with carb heat? I would bet that whatever air flow parameter is measured by the carb does not reduce - what merely happens is that the air is warmer which reduces the combustion efficiency.
In the present thread context, the question is why the application of carb heat fails to drop the RPM (assuming non-CS prop) if the engine has been leaned "excessively". I don't know the answer to this. I suppose that if the engine was leaned to (or past) peak EGT, and if applying carb heat really made the mixture richer, then the RPM would either not charge or actually increase a little. Can one get carb heat to INCREASE the RPM on an engine which has been leaned far enough?
So it's an interesting question.
Re leaning: contrary to very common belief, leaning does not cause engine damage unless it is run at high power, say 75% or higher. Lots of people are mortified of leaning during taxi for example - but it is completely and utterly impossible to do engine damage at 10-20% power or whatever it is. Lycoming authorise peak-EGT operation (the worst temperature case actually) up to 75% power. Detonation occurs before peak-EGT (about 50F rich of peak), right where people are likely to be cruising if using the carb heat method to check for correct leaning! But fortunately detonation cannot occur at power settings below 75% typically. Leaning past peak EGT is no danger because all the temperatures actually fall again. It is fine to lean way past peak EGT on the ground for example.