Connect LED from audio output without it blinking?
Ultimately, no, you can't keep the LED on steady.  Think about it.  When there is no sound at all, there is no power available to run the LED from.

You can harvest power from the audio signal and store any excess that isn't needed to immediately run the LED.  When the audio level gets too low to provide enough power to run the LED, you then use some of the stored energy.  However, any stored energy will be finite, so this can't go on indefinitely.