Does it make any differences if I adjust the drive chain on the center stand (or pit stand) vs. the side stand? Manual says on the side stand (for obvious reason).

No.
When you let go of the bike it rests or loads the swing arm lower.
When you rest the bike on the upright, this has a load on the swingarm and may rest lower than a side stand rest = Compensate that tiny bit is like do not even worry. Like the book said, find a high or tight spot on the chain and adjust from there.

I think a rear stand causes the chain slack to be a bit looser than it is with the bike on the sidestand.

http://www.zx14ninjaforum.com/messages.cfm?threadid=6AE7FFEE-D56B-84E2-15072A3BDDB69729

^^Check out the last few replies on this thread. I've tried it both ways and the rear stand seems to throw in another variable.

* Last updated by: Rook on 10/22/2014 @ 12:23 PM *

That is correct. My chain hits the mid pipe on the center stand; is quite loose; does not miss shifts; has no high spots; have adjusted the chain [after a tire change] to the point of landing at the same place since new. Go figure.

Yeah, with new sprockets and chain, I might have adjusted once in 20,000 miles. I always shoot for loosest specced slack. My chain is visibly drooping when the bike is parked on the center stand. It actually lays on the chain guide on top of the swing arm.