Define "survive". And you have a death sentence since you were born, so I think the only way of correctly discussing these things is in the terms of life expectancy.
I don't know exact numbers, but from what I remember there was one (or perhaps a few?) cases of people that defeated AIDS (that is, they no longer test positive). Those that test positive and are treated do live quite long - but I don't know if their life expectancy is identical to their peers. I strongly doubt, as there are no medications without side effects.