It all depends on the controller.
In the Centroid case, as they specify an encoder with an index pulse, I'd guess they are relying on the index pulse to synchronise moves, which if you're not threading, it likely doesn't serve much purpose. Without it, unless the controller continually counts the encoder, the controller wouldn't be able to synchronise for multiple threading passes.
The controller relies on you setting the encoder count in settings, and I would doubt if there is in any verification between the counts and the index pulse. There might be, but it's more likely to just show up as threading moves failing to start due to the lack of index pulse.

If you were to have more than one index pulse per revolution, then it's likely to cause synchronisation problems. If the controller is relying on the index pulse to start a synchronised move, then if there are four index pulses per spindle revolution, odds are not good for success.


I wouldn't worry about non-linearity problems on a lathe spindle. For basic turning, even if the spindle location varies by 10% over a revolution, it's going to have minimal effect on normal thread pitches. Even on a 2mm pitch thread, that's only potentially 0.2mm, which on a 2mm pitch thread, is neither here or there unless you're aiming for some kind of precision fit thread. A generic nut and bolt will likely have more play than 10% of pitch.