I will sometimes serge the seams if the fabric is delicate or has a tendency to fray. I would imagine that a whole quilt could be done on a serger. The seam allowances would be bulkier with the additional thread. A block pattern with strips or squares would be pretty doable. I'd probably leave the triangles/pinwheels/circles off of the serge list. The seam intersections would be mighty thick.

Let us know how it turns out if you try one!
Cathy