It is definately ok to have a pieced back.
I even have customers that piece their backing in such a way that the back was as beautiful as the front. You just have to ensure that if you used a piece top as a backing that the borders are WAY large enough to make it easy for the LA quilt to easily center your top on to the the pieced area. (It's like getting to quilts quilted for the price of one. If you have any questions about this method you can pm me.)