It's extremely unlikely that any strain of HIV will evade detection by either PCR or antibodies.

You probably misunderstand what's meant when we say HIV mutates a huge amount. Parts of the virus certainly do change wildly. but there are parts of it that stay very constant ("conserved"). And those parts have to stay constant, because they're what makes the virus a virus.

You can take a motorcycle and change its paint, swap out the handlebars, change the tires. You can even wrap it up in some lightweight costume and make it look like an X-wing starfighter for a parade, if you want. But if you pull out the pistons, or replace them with spaghetti, you don't have a functional motorcycle any more.

Tests for HIV don't depend on the equivalent of paint color or handlebars, they look for the functional components of the virus without which the virus can't replicate. For example, PCR tests often look for the Long Terminal Repeat (LTR), which are required for turning on the viral genes; these regions have minor variations, but can't change too much or the virus breaks.

The same is true with antibodies against HIV. Certainly there are antibodies against the rapidly-mutating regions, but for standard testing you don't look at those, you look at antibodies against the highly conserved regions.

(Why don't those antibodies against the highly conserved regions protect against HIV infection? Because, simplistically, many antibodies against any pathogen are not protective, and HIV has evolved so that the regions protective antibodies target do change rapidly.)