It certainly should mean that you're always online. Try this: 1) Close programs 2) Choose "internet connections" -> "Connect Automatically" -> "Always Ask" 3) Disconnect from whatever connection you're on at the moment. 4) Choose "internet connections" -> "Connect Automatically" -> <your_network_cell_provider> 5) At this point, I get connected: I have the circle with 2 arrows appear in my status bar. This means I'm online, even though no program is asking for an internet connection. What happens when you do this?
I don't use omweather, and based on that behaviour I don't want to. If I've disconnected from the internet, I want to stay disconnected until I say otherwise.
Simply: yes they do. What, are you billed for your internet by the minute? This was apparently an "always-online" device. For me, the only reason to be offline is battery life. And I usually carry a spare battery.