White noise shows no sideband-mediated detection ceiling for AM.

Evidence

Sidebands cannot be heard when using broad-band noise, because the long time spectrum of white noise remains constant, even though high-frequency amplitude modulation is used. Consequently for noise, the dependence of the just-audible degree of amplitude modulation on modulation frequency is not affected by the audibility of sidebands. — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 1021