Consider a hypothetical amp with 1mV of noise on the output and a 0 ohm output impedance. All of this noise will be heard in the headphones, and how loud this is will depend on their impedance and sensitivity.
If you were using 32 ohm headphones, and you added 32 ohms of output resistance, now there will only be 0.5mV of noise across the headphones. So this is a 6dB reduction of noise in the headphones. But this will also equate to a 6dB reduction of the signal(music) in the headphones too, so you will have to turn up the volume to compensate.
But turning up the volume control on the amp does not increase the amount of noise it generates. Well maybe just a bit, but nothing compared to the increase in signal - so noise is reduced. What you do lose is headroom though, as half the voltage swing of the output is being burned up in the output resistor, so 6dB of headroom is lost.
Of course i used as 32ohm phones with 32ohm output just to keep things simple, any other ratio of impedances will change how much noise is cut and how much headroom is lost based on their impedance ratio.
And this is only talking about the noise of the amp itself, any noise on the recording or from the source will vary proportionate to the amp's volume control, and will therefore not be reduced. So doing this can only help a noisy amp, not noisy source or noisy recording.
