I assume it does. If I had a big problem with that, I wouldn’t have connected it to the internet in the first place.

However, the talk about disabling printers without this update makes me think I should probably block it.

That’s a separate issue from requiring internet access / cloud / their servers to be online to print.

It’s not that difficult to go into your router and just block all external traffic from a device so yes I trust mine not to phone home.