Hi Philippe --
That's a great question. I can say that Go Button itself does not change its behavior when a device is running in Low Power Mode.
iOS on the other hand is a little fuzzier about exactly what happens in Low Power Mode. In general it seems like "discretionary and background activities" are what could get paused, things like networking calls and fetching mail, etc. If you have your device offline, these are not happening anyway. And Low Power Mode still prioritizes activities like playing music, so I don't think Go Button's playback would be affected.
My main concern would be that Low Power Mode might throttle the CPU. If so, this could affect playback if you are playing many audio files at once, or if your files are in a compressed format, since decompression happens on the CPU.
Doing a test run of your show beforehand would be the best way to find out exactly what might happen, since the device model, the iOS version it is running, and the condition of the battery will all be factors.
Brent