You can, but there might be a better solution. Since your border is pieced, can you insert a bit of fabric into the center of each side,making each side 2" longer? If not, you could iron some stabilizer onto each end of each border piece, making it 1" longer (at each end, so 2" overall), and then do the sewing. You will wind up sewing right to the corner of the outside edge of each border strip, but the stabilizer will strengthen it a bit, and when you bind the quilt that weak part of the seam will be covered.