I just tested it, to be certain. I clicked on the Airport icon on my menubar and selected "Join Other Network" and selected "Show Networks". The list of available networks popped up, with mine included, with a padlock beside it. As soon as I logged in, the padlock went away.
Well, the plot thickens! After doing some research, I just changed my wireless protection from WEP password to WPA2. After doing so, now the padlock remains, even when I'm connected! So WEP=no padlock. WPA=padlock. Go figure!