Does a device integrated through HomeKit still phone home?

[night python]

Hello,
I'm new to home assistant, and I wanted to give it a try because I'm trying to do more local contorl for my devices. Right now i just have a thermostat and two window ac units. The thermostat was homekit compatible, so I just added it to homekit directly. The AC's needed a custom HACS integration, but I also managed to set those up in homekit. Is this techincally local control though? If I cut the devices off from the internet, would they still work? Also, concerning VLANs, if I have a segregated LAN for IoT devices, and my home assistant rpi is on the IoT lan, could it all work with homekit so long as the rpi can communicate with a homekit hub on the main LAN? (HomePod or Apple TV) And would this provide any material benefit to security.