When AM is correctly accomplished (a single voiceband signal is modulated
onto a carrier via a non-linear process), at an envelope detector the two
sidebands will be additive. But if you independe ntly place a carrier at
frequency ( c ), another carrier at ( c-1 khz) and another carrier at (c+
1 kHz), the composite can look like an AM signal, but it is not, and only
by
the most extreme luck will the sidebands be additive at the detector.
They would probably cycle between additive and subtractive since they have
no real relationship and were not the result of amplitude modulation.

A peak detector is best understood in the time domain, try to create a
simple description in the frequency domain and you can only cause confusion
and incorrect conclusions.