Generally, I would bind before washing. However, on one occasion, the cat decided to pee on a quilt that I was working on. It was a queen size quilt that I was about 3/4 done quilting by hand. The smell was unbearable, and I seriously considered throwing it in the trash, but after spending over 100 hours hand quilting, not to mention over $200 in supplies, I decided to try and wash it.
Fortunately, even though it was not fully quilted, it was thread basted. To keep it from becoming distorted and frayed at the edges by the agitation in the washer, I put the quilt in a pillowcase, and took it down to the laundromat and washed it in a front loading machine.
Fortunately, it worked out quite well, and I was able to get the smell out and resume my quilting. Once it was completely finished, and washed again, you couldn't tell the difference in the areas that had been quilted before and after.
If you are going to wash it while in progress, I suggest you also put the fabric you are going to use for the binding to wash also, so so when you do bind it, the fabrics have all had the same treatment.