Microphone cues are great for the odd mic cue in a play, but I don't really think you can mix a musical with them with no additional hardware. And if you have additional hardware then you might as well have a digital desk.
The other thing about Microphone cues is that the latency you get will depend on the buffer settings of your interface in QLab preferences on the Qlab menu (not settings on the gear icon)
By default this is 512 which gives you a round trip latency of somewhere around 40ms, which is OK to a bit on the long side.
If you are only using a few simple sound cues with the microphones you may be able to reduce the buffer to 256 to give you around 22ms or even 128 for 14ms if you have a powerful mac. But you will get dropouts if you play anything that taxes the CPU like video or complex sound sequences or effects.
One other possibility is running MainStage on the same Mac as Qlab which can give you a more easily accessible interface which you can control on the IAC bus from QLab using MIDI Program changes and control changes.
If you only have an analogue board and you want to add mute automation using Qlab then you could patch the Analogue channel inserts in and out on your QLab interface
But unless you have to, or you enjoy having a miserable time, get a proper desk.
Mic