I think they are pretty important. Inside a bar, they protect your mics from smoke, etc. Outside, they eliminate wind-noise.
If you run without them inside, you won't run into any issues with sound, in fact you may notice better high end. However, if you run without them outside, you'll get wind noise. WN sounds like a rumble. If you've ever blown into a microphone and heard the "wooooof" come out of the speakers, then you know what wind noise sounds like.
Terry