Yes in theory I don't see why not, although the problem may be that people who have the disease do not know they do until many years later as it lays dormant in the system for many years.
So even if we thought we could contain it, cases would keep popping up outside the containment area.
Also testing people on that scale would be expensive and where would you contain them?
I don't know the exact number of people with HIV (i don't know if anyone truly does) but I read it is near the 35 million mark.
You'd need a small country to "confine" all those people.
And how would that be carried out and policed?
In theory, it might be an idea, but in practice I can't see how it would work.
Finally bear in mind viruses mutate, you never know what kind of HIV virus we will be tackling in the future or how it will spread