Am Demodulation - demodulate "double" signal- How

Hello to everyone! I am new to this forum and i don't have huge knowledge in electronics. Just the basics.So please excuse anything that may seem akward to
you ( i mean of what i write :blush: )

The question i have is :

Suppose we have two signals. Call them m1(t) and m2(t). We modulate each one
with AM modulation. So we get two separate signals (AM modulated). Those signals
have an Upper Side Band (USB) and a Lower Side Band (LSB) .
Now lets take the wave shown on an oscilloscope separately for each signal.
For the m1(t) we see on the oscilloscope screen a wave of the form shown in the
image below :

For the other m2(t) we see on the oscilloscope screen, a wave of the form shown in the image below :

now suppose we take the upper part of the m1(t) and the lower part of the m2(t) and
make a signal like the one below, and suppose that we transmit it to a receiver.

My question is...
Is it possible for the receiver to demodulate such a signal ? If yes... will a circuit (like the one on the below picture) do the work?

It seems to work , but i am not sure if its right or wrong...
Thank you in advance for your answers :D