Filtering and peak finding
Generally, this should not be possible because:


you project a 3D information onto a 1D signal, and the system is underdetermined in general,
you add a non-linearity (the norm), that further hinder restoration. 


However, using the triangle inequality, you can bound $B$ from below:

$$ \|A+B\| \le \|A\|+\|B\|$$

hence

$$ B_{\inf} =\max(\|A+B\| -\|A\|,0)\le \|B\|$$

In the example you gave, if the signals $A$ and $B$ are weakly related, outcomes can become interesting:

signal = (sum(C.^2)).^(0.5);
signalInf = max((signal-(sum(A.^2)).^(0.5)),0);
signalG = (sum(B.^2)).^(0.5);

plot(t,[signal',signalInf',signalG'])
title('Observed signal');
legend('A','Binf','B')




From here, you can recover putative peaks from $ B_{\inf}$. However, it is unlikely to work every time.

Could additional filtering help on $S(t)$? Without knowledge about the relative spectra of $A$ or $B$, I don't know (yet).