I don't see any reason why not. At times I have fixed some loose quilting that was pulling out on a quilt that had been washed many times by putting it in my sewing machine and going over that spot. Plus, a lot of quilters wash their fabric before they even start quilting, so it being washed isn't an issue.
The only thing I would watch is: if your backing and front is a little loose you might want to pin baste it in the area you are working on, as you go, to keep the backing from getting 'pinched' 'caught' and doubled or folded over while you quilt it.
Edited to add: nice quilt!
Last edited by quiltsfor; 07-13-2023 at 06:49 AM.