Years ago I tried fusible thread for this application and it did not work well for me. The problem is not what you think it is, as yes the fusible thread is strong enough to keep the line of stitching in place. The problem is that a single straight line of fusible thread is not enough to hold the binding in place once you iron. Fusible thread works best when it is in a zigzag pattern, which is not really feasible if you are sewing a binding to a quilt. With a zigzag, there is more fusible to melt when you apply the iron, so it becomes strong enough to hold the binding in place.
What I would advise instead is to sew the binding on as usual, then use Elmer's washable school glue to hold the binding in place until you sew. Sharon Schamber has an excellent video on Youtube showing how to do this. Basically you place small dots of glue on the binding, fold it over to where you want it, then iron to make the glue solid. This is trong enough to hold the binding in place until you sew, and the glue washes out when you are done.