By booking through Southwest you would NOT earn any hotel loyalty points nor would you get your status with the hotel chains because Southwest like Priceline is considered a third party. Now if you do make a green choice (declining housekeeping) or buy things at the hotel you can earn points for that. Some hotels will grant elite benefits when booking through a 3rd party but that is based on each hotels manager.
Now about the points plus hotels I'm sure they could change as partners change often but I'm not too sure as I book my hotels directly with the hotel chain as most offer a best rate guarantee so should Southwest's price be cheaper you can file a claim with the hotel and get more hotel chain points or a bigger discount (depending on chain)
hope this helps
Blake
