The structure can be treated anytime it will absorb the stain into the fiber rather than pool on the surface. Treated wood is saturated during the treatment process and must dry before it can accept stain. As soon as that drying process has occurred to the point you can apply penetrating oil stains. The easiest way to tell is to apply some stain in an inconspicuous spot and verify it is absorbed. Penetrating oil stain will not form a film and trap the moisture in the wood, so if its not completely dry, the wood will continue to breath without adversely affecting the finish. You may need to reapply in 2-years.