I can't comment on the standard Work Sharp, but I have a Work Sharp with the blade grinder attachment and I have put my BAS, baby villager CAK, and IBBB/MMB on it, as well as a few cheap non-HI khuks. It's a little tricky finding the right angle, pressure, and tension at first, and definitely not worth getting one just for a couple khuks and miscellaneous knives. I have put edges on those blades and other HI blades by hand as well, using stones, sandpaper, and just the chakmak, and only use the WS for user blades because it can leave marks.
To comment on what Karda said, when I put a khukuri on the Work Sharp, I typically start with the second finest grit belts and run it on very low speed, then switch to the stropping belt to finish. My goal is to take off as little material as possible, and basically just repolish the edge. I have produced a couple blades by stock-removal using this grinder, and have developed a good feel for it, and I still agree that it is neither the best nor easiest method. I used it on my hard-use blades because it's pretty fast (5-10 min vs a half hour) and it produces a good, strong convex edge, capable of shaving hair off your arm.
I recommend reading all those sharpening threads and practicing by hand first, and if you still feel the need to use power tools, start with a villager finish on a low angle.