I did not manage to find clear answers to this question: does decimation after an appropriate lowpass filter improve the signal to noise ratio?
To investigate this question, I considered data generated by a sine plus some random noise. The FFT shows a very clear peak (two with the symmetry). If I naively downsample without filtering, the signal gets aliased and the SNR decreases, which makes sense: I removed relevant information about the sine while keeping the noise unchanged. Then, I applied a lowpass filter to avoid aliasing when subsampling. The SNR did not seem to significantly change.
This question is of practical importance: when measuring a phenomenon, say at 1Hz, is it useful to use a very high sampling frequency such as 1kHz or more in order to improve the SNR by filtering and decimating (given that the memory and computational cost is not a problem, of course)?