The short answer is: No.
The longer answer is: The more a person waits before starting HIV meds, the greater their risk of having long-term health problems as a result of their HIV. But HIV meds are very powerful, and have helped people recover even when their immune systems are in extremely bad shape.
In a person who’s living with HIV, we usually measure immune health by looking at CD4 count—that’s the amount of a certain type of immune cell, called a CD4 T-cell, in your blood. CD4 cells fight off infections in your body, so the lower your CD4 count, the harder it is for your body to beat back those invaders.
A healthy CD4 count can be anywhere between 450 and 1,100. But in people who are living with HIV and not taking HIV meds, CD4 count will often begin to drop after a few years. If a person’s CD4 count falls below 200, they’re diagnosed with AIDS. That’s because research has shown that people with a low CD4 count are much more likely to get sick, and potentially die, from a whole host of infections and diseases that a healthy immune system would normally be able to fight off on its own.
Aside from the immune damage that HIV can cause, there’s also a lot of evidence that the virus can harm other parts of your body if left unchecked. Long-term HIV infection has been tied to the rise of heart problems, cancers, and even brain-related issues like memory and eye-hand coordination. Successful HIV treatment reduces the risks of all of these problems. (Unfortunately, it's less effective against another type of HIV-related issue, chronic inflammation, which can also lead to similar health issues down the road.)
All that having been said, it’s never too late to start taking treatment—just as it’s never too late to quit smoking, or to take any number of other steps to improve your health. There are plenty of cases where people have started HIV treatment with a super-low CD4 count—we’re talking single digits!—and have recovered, although in these people CD4 count is much less likely to rebound to "normal" levels.
Research also shows that, the higher a person’s CD4 count is at the time they start taking HIV meds, the less likely they are to develop health issues down the road. So the bottom line is: Starting HIV treatment is a very good thing, but if for whatever reason you begin treatment very late in the course of your infection, you can still improve and recover your health.