To reinforce Bens excellent answer, I set up my Tektronix TDS210 ($1000 scope with no probes connected) to 20mV/Div (doesn’t even go down to 10mV/Div) and 250us/Div (doesn’t have 200us/Div choice) and I found random noise (grass) of 0.6 divisions = 12mV. On the Nano (with no probe connected) with 20mV/Div and 200us/Div, delta-V cursor measurement = 4mV and 4mV noise viewable on the screen (0.2 divisions). I can also view ticks on the Nano screen from the frequency generator of the Nano with delta-V = 11.2mV. I know these ticks are from the frequency generator because they follow Freq Out changes on the Nano.
So the Nano actually performs better with less background noise displayed. Of course this may look better on the Nano due to the limited sample rate of the Nano. Your environment will also greatly affect these results. I have two computers running within 3 feet and that will have influence on the results.
Bottom line, the Nano is holding it’s own in this regard and this is not an issue.