Is the FFT magnitudes of multiple audio sources additive?
The FFT algorithm efficiently computes the complex valued DFT frequency vector $X[k]$ for a given time domain sequence $x[n]$.

The magnitude of the FFT output $X[k]$ for a given bin $m$ is the magnitude of the complex number $X[m]$, so like this :

$$X[m] = X_r[m]  + j ~ X_i[m] \implies |X[m]| = \sqrt{ X_r^2[m] + X_i^2[m] }$$

Now assuming two signals $x_1[n]$ and $x_2[n]$ with their corresponding complex valued DFT vectors $X_1[k]$ and $X_2[k]$, we can see from the magnitudes of complex numbers that 

$$| X_1[k] + X_2[k] | \neq | X_1[k] | + | X_2[k] | $$

hence the magnitude of FFT/DFT is not additive...