In a situation where the environment does not allow the patina to form, does weathering steel perform any differently than carbon steel?
Weathering steel is specifically designed to form a protective coating (i.e., patina) of rust that prevents the material underneath from corroding.
Referring to the Wikipedia article (1) on the topic,
Using weathering steel in construction presents several challenges. Ensuring that weld-points weather at the same rate as the other materials may require special welding techniques or material. Weathering steel is not rustproof in itself. If water is allowed to accumulate in pockets, those areas will experience higher corrosion rates, so provision for drainage must be made. Weathering steel is sensitive to humid subtropical climates. In such environments, it is possible that the protective patina may not stabilize but instead continue to corrode. For example, the former Omni Coliseum, built in 1972 in Atlanta, never stopped rusting, and eventually large holes appeared in the structure. This was a major factor in the decision to demolish it just 25 years after construction. The same thing can happen in environments laden with sea salt. Hawaii's Aloha Stadium, built in 1975, is one example of this.
The rate at which some weathering steels form the desired patina varies strongly with the presence of atmospheric pollutants which catalyze corrosion. While the process is generally successful in large urban centers, the weathering rate is much slower in more rural environments.
As you say, it would seem that your case, where the steel cannot fully dry, the protective patina cannot form.
My situation is a steel deck with a layer of aggregate on top. The aggregate will likely keep the top of the deck from ever completely drying or at least greatly slow the process. This will keep a patina from forming. Various people that I have talked with at the client have said that they would rather have carbon steel instead of weathering steel. They seem to think that it will perform better.
However, given the conditions you've specified, I cannot see how regular, uncoated carbon steel would perform any better than weathering steel in these conditions. I would expect that both will corrode approximately at the same rate in these conditions. My assumption is backed up by the information available on SteelConstruction.info (2):
Alternate wet/dry cycles are required for the adherent ‘patina’ to form. Where this cannot occur, due to continuously wet or damp conditions, a corrosion rate similar to that of ordinary structural steel must be expected. Examples include weathering steel elements submerged in water, buried in soil or covered by vegetation. If weathering steel is used in such cases, it should be painted and the paint should extend above the level of the water, soil or vegetation.
Regular carbon steel will be more cost effective than weathering steel, so I assume this is where your client's concern lies.
Personally, I would go with galvanized steel for the decking, or put some sort of epoxy primer over the steel (I assume stainless steel is out of the question).
1.) Wikipedia - Weathering Steel
2.) SteelConstruction.info - Weathering Steel