i don't have a serger, but if i did, I'd do it after i finished quilting because as many of already said, the quilt top will shrink up.

I just fold the extra batting onto itself and pin it so it won't be in the way.

You could try making your batting and backing a little to big then serge the raw edges of each layer. That would help prevent the fraying but allow for shrinking during the quilting.

You could serge just the top and bottom separatly to stop the fraying part but I agree with the others, the fabric shifts when you are quilting.