Loss of ground clearance could be an issue. As far as off-road and long travel with swaybars, some of the longest travel off road racer use swaybars:
The swaybars we use on Trophy Trucks are mounted upside down from what I've seen on most sidecars. The rear swaybar on the the #49 Herbst truck is mounted almost at the top of the "bed". It could be done the same on a sidecar too, but the bar would need to go through the trunk.