I don't think there is a compelling reason NOT to add a sub.
It would probably help with the 20-40Hz range measurably - particularly the lower harmonics from acoustic bass, for example.
Since you are interested in music and NOT HT, I might lean towards a sealed rather than ported sub. You lose the possibility of the very deepest frequencies, but probably attain some speed and control in the process.
I was very intrigued by this Carver
at onecall for $449. I damn near bought it even though I have a SVS PB12-ISD. Obviously, I don't know your budget for a sub. I don't think you could go wrong with the Axiom EP-500 or EP-600; even though they are ported, the DSP is apparently amazing. Also of interest might be the sealed models from AV123 and Adire Audio.
Unless your sub is actually making the CD player SKIP, I wouldn't worry about it. It's all 1's and 0's; either the player is tracking or it's not.
I don't think you should worry about "control"; anything you buy will likely have level and crossover settings on the subwoofer panel, so lack of bass management on the 3480 shouldn't really be an issue.
As far as placement goes, remember that even 6-12" relative to the walls can make a profound difference to your listening position. If you can get a little wiggle room, it might make all the difference. Of course, it's easier to get wiggle room with a smaller form factor.
I dig your message very much. Peace.