According to a recent report by Haoyan Chen et al. in Public Library of Science Genetics, it might.
From Charles Q Choi at Scientific American:
Researchers had noticed that some psoriasis patients had the same gene variants as people known as “HIV-1 controllers.” Such people have HIV-1, but they naturally maintain low levels of the virus and generally do not develop any obvious symptoms of AIDS.
To investigate further, scientists looked at more than 1,700 psoriasis patients and nearly 3,600 people who don’t have it. People who have psoriasis were significantly more likely to have the gene variants known to defend against HIV-1 and delay its progression to AIDS.
These findings suggest that psoriasis is a malfunction of antiviral gene variants that ordinarily protect us against disease.