Will a subwoofer add depth and clarity to my system, or just bass?

Subwoofers will not add clarity to a system. They will add impact in the form of notes you can feel as well as sound stage volume.

The problem with them is that very few people know how to integrate them optimally- including the manufacturers!!!. Getting a smooth frequency response with or without room correction is missing the point big time. Subwoofers need to be "timed" to your main speakers- synchronizing the beats at your listening position so that the pulse of the subwoofer is at its peak when the pulse of your main speakers are at their peak.
Getting the timing wrong will cause cancellation and ill formed notes.
Get them timed right (i use the New Order song Blue Monday") and it’s magic.  Just play the music and adjust the subwoofer continuous phase control in small increments until it sounds the best at your listening spot.  
If the sub does not have continuous 0 to 360 deg phase control- forget about it!  

@audiokinesis

Adjusting the continuous phase control provides much more than a slight amount of timing adjustment and my ears were quite capable of hearing when I had the correct phase setting. With such a range of adjustment it is possible to ruin the sound or optimize it with proper listening and technique.
Same for my car subwoofer- with time delay I was able to fine tune the proper delay relative to my main speakers and once you find the spot- car or home- the bass becomes effortless, deep, powerful and fully coherent through the range. The subwoofer then complements and works with your main speakers rather than fighting against them.  But again, the key technique was using beat pulses rather than pink noise.