Yea, the red light on the controller only indicates weather or not your sticks are active. Some games (very few) give the option to let you turn the sticks off using the button in between each stick and if you do that then the red light will turn off.
I dont think anything on any controller indicates online connectivity as far as I am aware.
PS: Just to second what ^ said, if the light on the controller is ever flickering then its loose wires, its almost never the game that makes it flicker.