In most cases the virus is still present. Very few people have been totally cleared of HIV.
The HIV community site HelpStopTheVirus has a good discussion on this and other challenges facing people living with HIV
It has been some time since I was involved with military medicine.
I do know that during OIF/OEF (our post-911 military Middle East adventurism) the army, at least, adopted the use of soldiers with low antibody titer Group-O neg blood as a 'Walking Blood Bank' (of course, being mil, it got acronymized as WBB). This meant if someone was wounded badly enough to require immediate transfusion, then the next name up on the WBB roster would be located.
Their blood would be drawn, and transfused immediately without any cross-match or disease screening. Indeed, going back to WW1 (The War to End All Wars) this was common practice in all the armies. Don't know that they were doing any disease screening though.
I do not know if the military still uses this system. If so, I can see the point, as live virus could be spread. However, if WBB is still a thing, it would seem a simple admin fix to exclude anyone with an undetectable viral load from being part of WBB, but still able to serve.
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