Most of the weight of standees is from their feet, which are on the floor, so they should be raising the center of gravity much.
I think just the added weight of standees makes the bus suspension less able to control sway and lean. Going into a curve or skid with more passengers means a better chance of rolling.
I've taken some curves with what we called a "full swinging load" that made my hair stand on end the bus leaned over so far.
Really busses can lean pretty far without going over. Another fun thing is if the air suspension bellows blow out on one side or a front tire blows out. Definitely gets your attention and not just because the passengers are screaming.
Going back to center of gravity, if the bus sways or leans on a curve and more of the passengers weight is transferred to the overhead bar that might make a difference, once the lean gets bad because of the weight in general.