Well I did some experimenting and the answer is:
Depends how smart the applications are. I tried xmms running straight from alsa, over the wrappers: artsdsp and esddsp.
Xmms insisted on doing it from the hardware mixer.
However I then used alsaplayer to play music and I could have mutliple instances of that open and I could control each instance's sound volume independantly.
So Linux CAN, but since alsa is new, or something, and we are comming out of the OSS (open source sound) dark ages were only one thing could be run at a time, most apps just use the hardware mixers.
This will change in time, of course, especially after 2.6 is mainstreamed, since this uses arts Edit: (crap I ment ALSA not arts) be default. (although it will still support OSS stuff)
You could probably use artsd to do it too, but you'd be restricted to only using kde-based sound apps. Which in itself is all that bad.