Any hickory backed bows I've made were intentional. With after-the-fact hickory backing of course, you'll need to plane or sand the back of the ash bow near perfectly flat. If there are any undulations in the existing selfbow, you'll have thin and thick spots of core wood, after flattening. Like Drums said, you'll definitely have to re-tiller.
If it were me, I would use the hickory backing on something like an osage board stave.