Antares Autotune AU plugins will not work as effects in Mic cues
If you just wanted chromatic auto tuning and didn't need t change set up for different numbers you can use it as a Mic cue output Patch plugin like this
In the Mic cue you want to auto tune matrix your Mic Input to a high numbered cue output e.g 24 This screenshot shows Mic 1 matrixed to Mic cue output 24

In Settings/Mic/Mic Patch insert an Antares Autotune Plugin in ch 24

In device routing matrix cue output 24 to device output 1+2 (or whatever outputs you are using for your PA)

Alternatively if you want to use presets then running MainStage and Qlab on the same machine is viable, and you can send MIDI Program Changes from QLab to MainStage using the IAC bus.
But………
Autotune is not an easy fix in most theatre situations, for the reason that Paul has outlined, and also because any spill on the auto tuned mic e.g other performers and band foldback which is in tune will then be detuned on that channel.
But give it a go. You can download 10 day trials of Antares AU plugins (but you do need an ilok to authorise)
Mic