It will not improve music quality to boycott, but destroy any shred of hope for the major labels ever releasing good music.
I just said, I buy smaller, independent label music quite often.
Out of curiousity, let's see what CDs I've purchased recently and what label they're on:
Neurosis' "Enemy of the Sun", "Through Silver in Blood", "Times of Grace", "A Sun that Never Sets", and "The Eye of Every Storm". All on Neurot Recordings, Neurosis' private recording label.
Battle of Mice's "A Day of Nights". Neurot Recordings.
The Pax Cecilia's "Blessed are the Bonds". Self-released (I donated to them).
Gojira's "From Mars to Sirius" and "The Link". Prosthetic Records.
The Mars Volta's "Amputechture" and "De-Loused in the Comatorium". Okay, I admit it - these guys are actually on a large label, BMG.
But that's it. Almost everything I buy lately is on indie labels.
So it isn't my fault that music sucks these days, and Justin Timberlake is a multi-platinum "recording" artist.