Does FFT magnitude of a sound drop to 1/10 of its value if sound level is decreased by 20dB?
-20dB corresponds to $1/10$ of the amplitude or $1/100$ of the energy. That's the same thing, since energy (all else being equal) is proportional to the square of the amplitude. 

It also corresponds very roughly to about $1/4$ perceived loudness but that's an entirely different can of worms