Yes, I do think washing will help remove the bearding. If it's loose fibers they should come off in the wash. The wash will also reduce the size of the hole the needle/thread have made during the quilting process so that will help as well.

Can't speak about the Valdani pearle cotton, I've only ever used DMC and I've not noticed any difference in thickness consistency. I honestly don't remember if I had a bearding issue or not when I used it. I've so far only used W&N batting and almost exclusively hand quilt - either with regular hand quilting thread or the DMC pearle cotton. I guess because I didn't know it was supposed to be difficult to quilt through the W&N I don't have an issue with it, lol.

I do a lot of hand quilting and have found that a sharp needle and smooth thread are a must. Textured threads like pearl cotton and yarn seem to love to collect batting on their way through the quilt sandwich. Since you've already started you could just keep going and use another needle or stiletto to push the batting back in.