I assume it's possible.
On Windows I dabbled in WinAmp+iTunes combo, with WinAmp for my music and iTunes for games. I would first sync my iPod with iTunes JUST for the games and then take it into WinAmp and sync the rest. With Songbird, I believe it's similar.
The only issue I ran into however, was that on my iPod, for example, fast scrolling through letters was thrown off because of this. So I would have artists like Aerosmith, The Beatles, Beck and fast scrolling would produce: "A" "T" "B" "T" "C" "T" "D" "T" etc.