I've seen cross stitch blocks incorporated into quilts a number of times, but I've never seen one after being washed.
I've seen redwork (all colors floss) blocks where the floss colors have run, and I'm wondering how the mesh would appear after wash.
Were it me, on a baby quilt which will be washed innumerable times, I'd do a full block test swatch with a throw away sample to see the outcome.