I washed a top without being quilted and did not have a problem (standard top loader with agitator). Here is a link to the finished top. It ended up being a practice quilt when I got my LA.
http://www.quiltingboard.com/picture...rm-t77776.html
However, I think I was really lucky that I did not end up with a big mess. I have read plenty of stories of others not being so fortunate.
Other things you can try to get the musty out
Hang out on a clothesline on a breezy sunny day
Seal in a trash bag with some charcoal briquettes for a week or two.