Hi Frank -
I often will bind my quilt before I finish the quilting because I get tired of dealing with the fraying and batting fluff while I'm quilting. I don't know what quilting you need to finish, but my only rule for myself is to finish any lines that would go under the binding before adding the binding. That generally means that I have done all of the stabilizing quilting on the inner portions of the quilt, but I would feel comfortable having that also pin-basted (or whatever basting method you use). So, if you keep everything stabilized, you should be fine. If you need lines that would go under the binding, then I would remove the binding since, with a normal binding, the fabric overlaps a bit further on the back of the quilt than on the front so you can't quilt up to the edge of the binding on the front without sewing over the lip on the back.
Sorry about your friend and hope that working on this quilt will bring you some comfort!