I'm just trying to separate the two concepts. Charlie said you need a sample of the "pitch" so I was clarifying that.
1) you can pitch shift without determining the frequencies being played as described above. In fact, it's very easy, but doesn't necessarily sound very good.
2) to compensate for the artifacts that are created if you do the most basic pitch-shifting, which has essentially 0 latency, you need to introduce computing to try to determine how to minimize those artifacts. Even then, you're probably not looking at the freqeuncies of the notes being played. More like the general shape of the nearby samples to try to work out how to adjust for the dropped samples with minimal artifacts. Now, that data does include the shaping caused by the frequencies being generated, but you're not inherently looking at the frequencies themselves.
It definitely does need some detail in order to minimize artifacts indeed. It's why polyphonic pitch shifting can get a bit warbly but still not sound like complete trash, because the more notes you have in the input, the more complicated it is to work with the wave.
Not only does having a pitch shifter assigned to each string allow you to tune each string individually, but it helps the Variax pitch shift with better results.
Either way, the latency is used as a fallback to have time to tailor the signal into a good quality pitch shift.
The best VST pitch shifter I've seen is called Pitchwheel, and that needs 46 ms to do high quality pitch shifting. It sounds remarkable.
Reaper's ReaPITCH also is high quality and has high latency.
The less latency, the less natural and professional the pitch shifting will sound.
For the Variax, you need a good balance between latency and quality. Fast enough to not ruin your guitar playing, but good enough quality for it to pass as capo/detuning substitute.
I say the Variax does a nice job.