Running the LED display takes a certain amount of CPU time, as would running spectrum analyzer code, so while I am certain that it can be done, I am not certain *how fast* it would be.
You might begin by looking at the Peggy2 library for Arduino and the existing FFT spectrum analyzer code out there; here’s an example that might be a good starting point to look at: http://blog.arduino.cc/2010/11/16/arduino-realtime-audio-spectrum-analyzer-with-video-out/
