The "conventional wisdom" I've always heard, and my own experience seems to support, is that your immune system is strengthened when you're on. Sometimes you hear (again "conventional wisdom") that your immune system might drop off a tad sometimes when you go off. Again, I don't remember ever getting a cold or flu or anything while on, but once or twice over the years I've caught a cold or something (never any big deal) after I come off at the end of a cycle. Have no idea if their is any scientific basis for any of this, but like I said it does match my own experience after about 20 years at this.
Also, like OTH says, they prescribe AS all the time for people who are HIV positive, or have other immune system problems, and it seems to be pretty accepted in the medical community that it helps. As for sleep, I think its pretty well known that high dose AS can sometimes cause difficulty sleeping. I don't think it has anything to do with WHAT you are on, test, EQ, Winny, or whatever. I used to have this problem, but as a few years have gone by, don't seem to anymore. Again, no idea what the scientific basis for this is, or if anybody knows. You don't want to get to used to taking something, but I took an ambien at bedtime off and on when it happened, and that seemed to take care of it.