You can, and it's commonly done - although there's no particular need to calculate the average in the processor, simply use the processor to display the input. The input needs to come from a rectifier and suitable attack decay circuit, just as with any other VU.
I did this years ago (2003 actually!), using a 16F876 to create a stereo 16 LED version of the LM3914/5 - with switching for lin/log and dot/bar. To do the log scale I used a log lookup table, created using a little Delphi program.