Well, considering that anavar is given to AIDS patients, I don't think that it would compromise the immune system.
I just found this study. It seems that the type of steroid makes all the different WRT immune function.
J Steroid Biochem Mol Biol. 1990 Sep;37(1):71-6. Related Articles, Links
Anabolic steroid effects on immune function: differences between analogues.
Mendenhall CL, Grossman CJ, Roselle GA, Hertelendy Z, Ghosn SJ, Lamping K, Martin K.
Department of Medicine, Veterans Administration Medical Center, Cincinnati, Ohio 45220.
As an untoward effect of chronic anabolic steroid use, immunologic alterations may be induced. To evaluate this possibility five commercially available steroids with various types of structural differences were studied in male Sprague-Dawley rats. Animals were divided into five groups and treated with testosterone (Group 1), testosterone propionate (Group 2), testolactone (Group 3), oxandrolone (Group 4), and stanozolol (Group 5). Androgenic anabolic steroids were administered daily, subcutaneously dissolved in oil, at a dose of 1.1 mg/kg. Immune alterations were assessed by skin-test responses to phytohemagglutinin. After five days of treatment (1.1 mg/kg/day) a significant immuno-suppression was observed with all groups. However, by day 10, groups 3, 4, and 5 showed an immuno-stimulation. Using oxandrolone as the model stimulant, serum testosterone levels were significantly suppressed, while castration abolished the stimulatory effect. These observations indicate that immune alterations do occur with anabolic steroids which are immuno-suppressive when the steroid nucleus is intact and immuno-stimulatory with nuclear alterations. It appears that these changes are associated with altered gonadal testosterone release.
PMID: 2242353 [PubMed - indexed for MEDLINE]