I do a lot of wall hangings using fusible and I always finish the edges in some fashion so that the fabric is sewn to the background.
There is fusible that says "No sew", so be careful what type of fusible you purchase. I believe that type is more for banners and that sort of thing than it is quilts? (Can anybody correct me on this?)
Hope we get more info so we can help you complete your project!
Watson