Sure-- I almost always piece my borders.
Depending on the style of your quilt, it could look really interesting to add a thin strip of contrasting fabric at the join -- make it a feature, rather than something to hide. Or if it bugs you to see it, maybe having some applique cover it, or have a block of pieced work break out into the border.
To me, the fabric limitations are invitation to be creative with the design. Some of my most favorite features in quilts are the spur of the moment innovations.
RST