I'm not sure what you would accomplish by not binding??
...... if you are washing whether with or without binding, you are going to have a washed quilt.
Agree with the others, that you either need to do your fix-up now ... before washing.
Or decide to live with it .... bind it, then wash.
If it is bothering you now .... you are probably best to do some reverse-stitching and re-do your quilting in your area of concern.