Oscilloscope averaging and standard quantum limit
Yes for random noise Vrms keeps reducing by N for sqrt N samples


the SNR is then limited by drift, periodic noise and measurement accuracy 


other


However, if the measurement is a frequency which is nearly as stable ( high SNR) as the clock in the counter measuring it, then some phase noise must be added in order to obtain an accurate reading. Then the noise can be defined by std or pp deviation or Hz/rt(Hz)


This can also be done by adding some AC voltage with a fixed trigger threshold. 
with  sqrt(N) more samples you obtain N-times better resolution and stability on the result just as in DC.
This AC exception example is due to harmonically-related synchronous effects with no jitter.