A new form of modulation?
Anyhow, my question, what if we did not assume that? 


Demodulation is still possible, but much harder, so much harder that there is easier to transmit the signal without any modulation.  And that is for a single signal.  And obviously one is using modulation so that we can carry the signal using other frequencies than those of the signal itself (so that one multiplex several signals, or because those frequencies are too noisy to be usefull), and that would not be true in your case.