Yes, I run with the channel grounded (GND coupling), but that was just to measure the noise level, which BTW was about ~65uV std deviation (in 8 bit mode), slightly better than the specified 80uV (@500MHz BW). But mine being BW limited to 100MHz probably also helps a bit.
Imho, this is not right for measure base noise level including whole pathway from input terminal until you know exactly how this couplin is done in circuit. In some scopes it may be even so that it only close ADC output or ADC input coupled to GND or what ever kind of fake "GND coupling".
It is partially right if GND coupling is first thing just after input BNC but my guess with some experience is that it is not. And even then it do not remove all possible DC bias and due to this RMS value do not tell just noise level.
But we are interested about whole front end noise starting from BNC and ending to ADC binary output..
Imho, best way is measure noise level is: After well done selfcal.
Lowest true full resolution V/div.
Input coupling DC (or AC but still need care possible small internal dc offset before ADC and in ADC)
Maximum samplerate, maximum memory (maximum true measurement data and here need remember some scopes may use very small intermediate buffer and because noise is random it of course may affect result so that apples apples compare is difficult)
Bandwidth used for measurement is important specially if compare others. All know noise and BW relation.
For measurement avoid RMS measurement if possible. If can not use better then need take manually care about possible DC bias correction calculation.
Example with 500uV/div this DC bias may give lot of error. Instead of RMS use Stdev what leave DC out aka "RMS without DC".
(All scopes do not use all samples for measurements so if this is case it need note.)
It is also good to compare noise measurement using open input (and if need, use just BNC Open cap (not short!) for block external noise.) There must not be big difference. If there is big difference, hidden reason behind it need find.