Hi Nick,
You wouldn’t be connecting your audio equipment to the public wifi, or to the internet. You could actually do this, which would involve running a network cable from your mixer into the venues access point, if it had a free connection, but then everyone on the network could connect to your mixer if they had the app. 🙂 You could also see a drop in network performance when the audience showed up and started facebooking etc.
What you do is buy your own access point, connect it to your mixer with an ethernet cable, and then connect your ipad to that network. You may have an old ISP provided router lying around which will be fine for testing, and for small events.
I use a TP Link WD8980 for various things, which is about £30 on ebay. I’ve never had any issues with it.
Chris