I always quilt mine before doing the binding, but I have also quilted one that has originally been tie knotted. It turned out good. I had no problems with the back puckering either. It was a first time quilt that was done by a distant family member and someone spilled soda on it and she wanted to wash it. But...............the batting she got was cotton so washing it without close stitching was not an option. I have a hobby longarm so she asked me if I would do it for her before she washed it. As I was doing this, I thought to myself that this is a good way to quilt it. I have one that was done years ago that was tie knotted and I have been thinking about putting it on the frame and machine quilting it also. I don't know if putting a binding on a home machine and trying to quilt it would be a good idea because of the fighting with the bulk of it. On a frame it is pulled tight.
Barb