Yes, you can add a backing after you've already finished tillering it. It's not the most common practice, since a backing will normally be used for iffy wood that would otherwise break without a backing. But if the bow survived without a backing all the way to full draw, you don't need a backing clearly. However, a backing can still be applied to make a bow look better, or to make it more safe and durable. It's also a good way to greatly increase the drawweight. A wood backing will easily increase the drawweight by 15-30 pounds. Still, you will need to re-tiller the bow after applying the backing. Don't expect the tiller to remain the same as before applying the backing. Another thing to consider, is the fact that glueing a wood backing to a bow that already has its corners rounded, is tricky. You can only glue down the flat back, and not the rounded edges. Of course, this only applies for a wood backing and not for sinew, rawhide or silk, which are flexible. Also, if the bow has already been sealed with oil/varnish/wax etc. you cannot glue any backing onto it.
By the way, what exactly do you mean with 'laminate backing'? You don't mean a laminate flooring, right?
