I think it would depend on the speed during a turn and probably other things. I remember a thread about the SR having a tendency to turn-in when leaned during a turn, so I was looking for it this morning on my way to work. Indeed, if I just let go of the handlebars during a turn at a slow-ish speed, around 30 mph, the front wheel was turning into the turn, resulting in the bike trying to go wide/straighten-up. I would not say I feel it when I'm just turning, but letting go of the handlebars illustrates that point.
That said, I had a 55L top box on the rack with about 6lb in it (so nothing too heavy). And I have to try the same experiment without the box and at different speeds to know if that tendency continues and if it gets stronger or weaker... But it is like the front wheel wobble thing - you let go off the handlebars and it happens, you put just a slight touch, and it is gone, so one may never feel it or mind it in normal use.
Coming from bikes with a more relaxed geometry I think I've been used to bikes that simply hold a line while in a sweeping turn. In contrast, on the Zero S I feel like I actually have to expend mental energy to steer the bike around a turn. It feels twitchy and overly sensitive to rider input. I've gotten used to it (after 7000 miles) and the PR3/PR4 tires have helped, but that was definitely my first impression.
My S handles pretty much exactly like the Buells I've owned. I guess I shouldn't be surprised because that's where Abe Askenazie got his start before moving to Zero.