OK, let's throw simple logic at this question. Anyone who's ever tried to maximize audio density on an AM knows that if you "use up" your
modulation with sound that is too peaky in one range of audio you will not be able to modulate others nearly as well.
By everything I learned about high level mod, ANY modulation sidebands added will result in less of the carrier until at full modulation, all the power (plus any added power from high-level mod) will be in the sidebands.
This isn't done for clipping's sake, but is approached as nearly as possible without clipping.
Now, if we add considerable modulation products up to 15khz, even at the very low % of power, it is still full-time, and must result in
less power for something else. The common node current won't change, and the FI readings won't either, unless you can set a passband that's really looking at only the carrier, and not adding in the energy of the sidebands, which will sum to show no net change.
Even given that the energy for the HD sideband may completely sap the equivalent coverage away from the analog signal, and it probably can be proven given what I suggest, the level to listeners is probably only -2 db, or marginally perceptible.
Most, even the cheapest radios have so much reserve gain that natural conditions account for far greater variance in signal strength.