I believe all that the "fan" icon is indicating is the strength of the signal between your computer and the wi-fi device. In my home I have two wi-fi devices that I can connect to and several others in my neighborhood that are visible. A few have only one or two bars visible in the "fan", which indicates to me that they are a far distance away or there is significant mass between us that weakens the signal.
My wi-fi set up includes two wi-fi networks, 1) an AT&T Router that is connected by cable to the AT&T system, and 2) an Apple Time Capsule that is plugged into the AT&T Router so it emits a second wi-fi network which I normally use. So that my computers can automatically back-up to the Time Capsule. I just ran this test... I unplugged the ethernet cable that connects my Time Capsule to the AT&T router. The Time Capsule network still appears to be a full fan signal strength. But when I try to open a new page in my internet browser it displays a message "You are not connected to the Internet" message, or a blank page. There is a yellow light displayed on the Time Capsule device now, its normally green when all is well.
If I choose the AT&T router network, I connect to the internet fine. If I go back and try to use the Time Capsule network, which is still displayed with a full fan symbol in the Menu Bar, then after trying to connect and failing the fan icon changes to an exclamation mark "!". Oddly when I click on that to select another network the pull down menu, that is displayed for the Time Capsule network, still shows a full fan icon. I interpret all that to mean that all the "fan" icon indicates is that its possible for me to establish a strong connection between my laptop and that network. But it does NOT mean that the network downstream is functional or working. If you run the "Wireless Diagnostics" at that time I believe it will tell you a little more about where downstream the Wi-Fi disconnect is occurring.
