It depends on the type of free public wifi. The ones that just let everyone on without having to click an acknowledgement first, yes, you can use those just fine.
Some require that each MAC address (individual device) click an agreement that it won’t be used illegally, etc. Since the camera can’t surf to the agreement page and click the agreement button, it can’t use those free wifi options directly. But there is a loophole.
If you have an old cell phone, you can log on to the free wifi, then turn on the hotspot option on the phone and the phone will then act like a router for you to connect the camera to, which then relays everything through the free wifi. I am actually doing this exact thing right now on my vacation in Hawaii…I connect a phone to the wifi which requires acknowledgement before it will work, then I turn on the hotspot and connect my Wyze cam and other iot devices to that phone hotspot and everything works.
(I also run a VPN on the phone so that everything is encrypted and nobody can access any of my data… So I might suggest running it through a Phone’s hotspot with a VPN anyway even if it will connect without it… If you don’t have an old phone, ask friends or family if they have an old one with a cracked screen or you can buy them really cheap anyway… if not, it’s probably five if it’s not recording something extremely private…)