Larger front tire or forks lowered in the tree will make the rear tire closer to the ground on the stand (and vice-versa).
Larger front tire, lowered forks and/or higher rear shock pressure all increase CS pivot height and therefore make getting up on the stand easier, all other things being equal.
Tire clearance doesn't necessarily tell me much about CS length, it does tell me about the hassle-factor to pull the rear wheel when on the stand.
As an aside (but absolutely related to the topic), with a helper present, put your bike on the CS and drop the air pressure in your rear tire a LOT as if you have a puncture. You'll likely find the sidestand is dangerous or useless, can you hoist the bike to the CS? What do you do when your loaded bike gets a flat on the road, or goes flat overnight and you don't know it 'till you roll it off the CS?