You can ABSOLUTELY piece your border together! One thing you want to be careful of is that you don't have any fabrics cut on the bias or crooked to the point where when you sew them they will shift and cause puckers. Although many quilts have such elaborate tops that they borders are created out of strips for simplicity, a great number of quilts also have pieced together borders. Ultimately, anytime you sew fabric together for a quilt, you are essentially making just one new piece of fabric, so it shouldn't affect your finished product!
