I usually quilt close to applique pieces before quilting the background. But I am working on a quilt with a "zillion" little pieces appliqued. Can I omit quilting around the pieces and just quilt the background?

How are the appliqued pieces attached? If they are sewn on, I don't think it would be a problem. If they are attached with a bonding material, I would think they would need to have some sewing done on them, especially if it's going to be a quilt that will be washed frequently.
Just my opinion.
Carol B

You can quilt an outline around the entire applique (instead of each piece). You can even simplify that outline if you like. You don't have to quilt around every little piece.

I've seen a lot of quilters just do close filler designs up close to the appliqué, highlighting the pieces without having to actually go outline the work.

I do alot of needle turn applique. When quilting the quilt I never quilt on the actual applique, just around it. My quilts are washed frequently a I never have a problem.

as long as your appliques are stitched down you do not need to quilt them too. but they do need to be sewn to the background. most fusables will not hold up to washing, stitching is needed in one way or another