Electronic – Interface telephone handset

Music is a special case for audio latency. For speaking, or voice conversations you can have up to 100mS latency before it impedes the conversation - though it can be noticeable at that latency. Music, however, has a beat and 100mS is unacceptable.

When musicians play together acoustically sound travels about 3mS/meter. On a typical stage setup band performers would deal with maximum 25mS of acoustic delay. Larger stages require monitor speakers with maximum 10mS latency so the acoustic delay is always under 25mS.

As long as your system is expected to provide feedback (monitor) to the musicians, and they are close together, or they have low latency monitors apart from your system, and the band is fully amplified - ie, the audience won't hear both the acoustic sound from the band and the amplified sound from the speakers - then you might get away with a larger than 25mS latency for your entire system - from music pickup to speaker output.

However, it's likely that the band can hear the amplifiers, and again any delay greater than 25mS is going to cause them some aggravation.

With small, frequent UDP packets you can meet this over wifi, but it's going to be tricky accounting for all the sources of latency inside such a setup.

Go ahead and do some testing - use one Pi with a microphone, one with a speaker, and both with wifi. Have them simply relay sound from one to the other along the full path, from the mic to the speaker with all the bits and pieces in the middle. Capture very small packets - 1-5mS each at the most - and send them across. Use an oscilloscope to measure the latency. I'm guessing with USB sound devices and USB wifi devices and the stock non-realtime Pi you're going to see very large latencies. You'll likely have to do quite a bit of investigation and work to bring them under 25mS.

There is the assumption that if most gigs have clean sound without a DI box, then there should be no problem. Until the day comes when you have hum in your signal and maybe buzzing noises from stage lights.

It is worth it to have a simple passive DI box on hand just in case. These have an isolation transformer with a high-impedance input and a 200 ohm differential XLR output that makes it immune to noise, even if it is a 200 foot run to the sound tower.
This article helps with the history and adds more details.

Purpose:
The direct box takes a high impedance, unbalanced signal and converts it to a low impedance, balanced signal. This allows the signal to be sent over long cable runs with significantly less signal loss (especially in high frequencies) due to the lowering of the impedance, and greater rejection of interference due to the benefit of common mode rejection in a balanced signal.

Furthermore, the lower impedance (around 600 ohms is normal) allows an insignificant load to the input of a mixing console or preamp which is also designed to accept input from low impedance microphones.

There are battery powered versions for microphones that need phantom power and/or a gain boost as well. You may not need a DI, but if you do and you have one it can save you from a disastrous gig.