This way you do NOT have to rig and animate it. Basically you just use vertex painting (which I didn't even know what that was before the video) to paint weights on your object in maya. Then in UDK you can animate it using vertex's.
So basically you paint it two colors from top to bottom, lets say the bottom is blue and the top is yellow. You set it up in udk that the color blue, which is the base of your plant, is affected 0% by swaying effects like wind, and that yellow, the top of your plant, is affected 100%, everything inbetween of course is affected 1-99% and gives a nice swaying effect, with the bottom of your plant staying planted and the top swaying. It may sound complicated but is extremely easy.
I'm not overly familiar with UDK so I can't suggest another way too animate, other than importing a rigged, animated object. However I can tell you the way I described it is the way all the plants in the engine are done.
It's a pricey tutorial, I can't really recommend anything other than saving up for it, it is definitely worth it. And I followed the tutorial's using the newest version of UDK back in October, so you would have no problem with it.
Hope this helps, all I can say is save up for this one, if you are a newbie to UDK like me, it is more than worth its weight in gold. Just buy digital copy, its half the cost of the hard copy.