Yes, and you can do something similar with bandpass filters (they aren't adjustable in a spectrum analyzer) but that's a LOT more complicated.
The MSGEQ7 is pretty-slick little chip that makes the hardware and/or software super simple (when it works).
The MSGEQ7 datasheet says, "Seven Band Graphic Equalizer" but that's NOT what it is... It's a chip for making a 7-band spectrum analyzer which could be built-into a graphic equalizer.