Would a computerized quilting machine be able to go over ons and snaps on a quilt?

I've made a quilt top consisting of my son's baby clothes and have left some of the details (ons, snaps) on some of the squares for added "texture," if you will. I'm at my wit's end with trying to machine quilt it myself on my cheap brother sewing machine...I've tried stipple quilting and have followed all of the instructions (lower feed dogs, use darning foot, correct thread, etc) and am having a ton of trouble with my stitches looking even and consistent. I'm sure this just takes a ton of practice and a better machine. So...I'm exploring options to have it professionally machine-quilted and wondering if they'd be able to do it with the ons and snaps that could get in the way? Thanks!