Exterior grade plywood is typically used as a substrate for decks or balconies that are above living space where weather protection is a must. The protection is not only important to the dwelling below, but will also maintain the integrity of the plywood and keep it from rotting.
Needless to say, carpet will not offer any kind of weather protection and when soaked with water will speed the deterioration of the plywood. Rolled roofing or other built-up roofing systems are not designed for traffic. Furthermore, roofing products in general don't offer the kind of appearance that one would typically prefer for a deck.
Good News! We know just what you're looking for: an elastomeric waterproofing system. In simple terms it's a seamless and skid resistant synthetic rubber coating system that is designed to be installed directly over exterior plywood or concrete decks. It cures in place to provide an attractive finish for surfaces that are both floors and roofs.
One of the most positive aspects of the elastomeric system is that it expands and contracts with the substrate avoiding cracks and other damage resulting from movement. An added bonus is that many of these systems are available in a variety of colors and textures and with slip resistant surfaces. Due to the complexity of installation, this is a project that should probably be reserved for a professional.
For more information on elastomeric waterproof decking systems write the folks at Gaco Western Inc., P.O. Box 88698, Seattle, WA 98188 or telephone (206) 575-0450.