Chains are best adjusted when clean, lubed and warm.
On a stand is always best, as lean stands beg for leaving it "may be OK to OK" as compared to ease of getting it "just so" re slack and alignment when on a stand.
Race stand preferred.
Centre stand is very OK to use, as long as you make an allowance for whatever the change in slack is for any given bike on or off the centre stand.
Slack should be set for the tightest spot.
Slack should only be checked after a spin, not just after an adjustment screw movement. ( a wheel spin on the stand, if a lean stand, pull it over on the foot and get a helper to spin the wheel for you)
Modern day quality sprockets are so much better than many years ago.
The front and rear radial runouts would combine to net wide ranges of slack over many wheel revolutions.
I have found little variance with my 919 or the GSX-R in this regard.
Personally, my opinion is that slack set tighter than half way through the allowable range is not desireable.