With some smart TVs, no. For example some Vizio TVs require you to install the Vizio app on your phone (you must allow location tracking) and connect over WiFi before you can even finish the setup process.

Usually, but some won't let you finish set up without some internet access.

Even if you do keep it disconnected, there's no guarantee that a badly behaved update process or app won't interfere with the normal operation in some way.

I'm sure there do exist models that are perfectly fine in offline mode, but it's still a lot of (very opaque) room for things to go wrong in ways that a "dumb" display won't have.

That's what I usually do.

But, even then it can be annoying. If I happen to press on the smart key on my remote, by mistake, the TV then takes ages to check that indeed there is no connection, with a large and unescapable message dialog.

Bad design decisions all around.