Yes, you can definitely use your piecing thread for quilting. I do it all the time. It will not show up as much as a heavier weight thread, but it will still work perfectly nice to hold together the layers & many novice quilters prefer that as it hides imperfections better than heavier threads. I would make sure that if you are using a cotton thread, that it is at least 50wt for the quilting ("at least" meaning 50wt or lower since thread weights increase in size as the wt decreases).