it will add strength in the same way adding another layer of wood will, of course it will not add as much strength as the carpet is not the best media for absorbing resin and is not nearly as thick as another layer of wood, but it WILL add strength. It will also not affect the 1/4 wave function inside of the box. Adding bracing to an already built enclosure is not easy to do, threaded rod will be easier but still needs to be included in the over all design of the enclosure. Being that you are on team SSA I'm just going to assume that you follow Pound that Sound's (thumpper) builds and that is where your love for bracing comes into play.