Not inherently, no. I'm building out my home automation with mostly ESP8266 based sensors, relays, modules etc. About half of those are NodeMCU, the other half are commercial devices flashed with custom firmware. My biggest "win" so far is taking over thermostat control of the whole house ducted AC. I now have it automatically change which room it prioritises temperature stability based on presence and time of day (when the child goes to bed).

My system "relies" on an internet connection for just one thing right now: iPhone push notifications, which are merely informational and mostly for debugging. It also uses the internet to keep my local NTP server in sync. When I'm away from home I can manually check on stuff with a VPN.

In future I plan to expose a minimalist HTTPS api for triggering certain actions remotely, like the garage door. But even that's not a big deal right now because I've got a outdoor AP that covers a wide area outside my house—my phone is generally already on wifi as I approach home by foot.