2 inches is definitely enough if you have a thin to moderate loft batting. It would not be enough for high loft. What you might want to do is make a test quilt out of some scrap fabric (using the same batting as is in the quilt), cut a 2-inch strip of scrap fabric, and make sure it's going to work for you in terms of covering the edge adequately. You will want to keep a 1/4" seam and miter a corner on your test.