Nope - not automatically - you can only manually request to display the URL...
Actually I have to admit that I thought the "auto startup" mode would just be used by people who have fixed IP addresses in the office/at home... In any other case it would be anyhow quite dangerous to start the server in a WiFi environment that is "unknown"... since you don't know with which people you are starting to share your data...
Personally I only start the WiFi Server manually while I am at the office - and use the WLAN-based (SSID triggered) autostart mode when I am at home.