Afraid not. (Possibly you have one of the very expensive models with Sideshow - a display on the "outside" face of the laptop - but even then I suspect not). The button only turns the wireless connection on and off (it has to be on to allow internet connection). Most laptops have them as it saves battery power to turn off the connection when not in use.
Mind you, laptops will generally remember its last setting, so if the wireless was "on" when you turned off it should automatically come on once everything has loaded.