There is a page of a list of plants that other BYC members have successfully grown in their runs and verbena is on that list. You will probably have to provide some protection for it, at least until it gets established. I have rosemary and lavender growing outside my run and grapevines inside and over top.
I hadn't even thought about growing any plans in/around the run. I have two young grapevines, but I don't think I want to put them where the flock can get to it...or else we'll have no grapes for ourselves. But the ladies will certainly enjoy the fruits of our vines, once the grapes start growing.
You only have to protect them from the chickens during the first month or so of growth so the tips of the vines get out of jumping height. I have three grapevines inside the chicken run, we get all the grapes we could possibly eat and make raisins out of the rest. After the vines really get growing in summer, the chickens get all the grape leaves they can possibly eat.