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

Umm ...

To OPTIMALLY separate the (low bass) subwoofer passband from the (mid-bass) main woofer passband, it's necessary to use a full 4th order (24dB/octave) active Linkwitz-Riley crossover.

The electro-acoustical sum is what matters, and it's more than just what you remove, it's how the subwoofer integrates with the rest of the system.

This is why THX used a sealed 80 Hz limited satellite as the standard.  Add 2nd order high pass filter, and voila, you have a total 24dB/octave roll off which would integrate nicely with a sub using a 4th order electrical low pass filter.

Honestly, only speaker makers and active room correction software does this anywhere near optimally, which is why I'm wary of recommending subs at all. It's not the tech is bad, it's the complications in the setup that I've so often heard as poor.

Best,
E

I've chosen a 7th order (42dB/octave) Linkwitz-Riley low-/high-pass at 80Hz for my tapped horn subs and all-horn mains via a Xilica XP-3060 digital XO - it's simply what sounds the best. 

Previously I ran my mains full-range with a single SVS SB16-Ultra low-passed at 61Hz 24dB/octave (via its own build-in DSP), and while this pairing integrated very well my new setup with two tapped horns (powered by a Crown Macro-Tech 1200) and managed by the Xilica unit, now high-passing the mains, even at this rather early optimization stage sans PEQ offers better, indeed seamless integration with the mains, while lending the presentation a sense of uninhibited "breath," ease and coherency not heard with the previous single SVS-installation. 

Aspects of this no doubt falls back on the inclusion of not one but two tapped horns, but running the mains full-range, by-passing the Xilica, with a lower ~60Hz low-pass of the TH's tells me all I need to know with regard to my preference; to my surprise even running the Xilica over the mains with a high-pass isn't detrimental in regards to transparency, but has a freeing effect on the sound with noticeably better energy-coherence and overall integration. If there is something robbed of nuance via the Xilica, I'm not hearing it (in indication of how good a digital XO it really is), masked perhaps (perhaps not) by the other qualities it brings to the table with the high-passing of the mains that only adds to the enjoyment and insight of the sound. 

In not trying to make a case with the above as a generalization of what works the best in every situation (certainly, it depends), but simply to highlight that the typically non-audiophile approach of steep filtered, high-passing of the mains in the 80-100Hz region can work extremely well - with a pair (not four) of symmetrically placed tapped horns, no less, and in stereo mode, God forbid.  

In my humble estimation, a subwoofer adds those bottom resonances and harmonics that otherwise would be missing. Any subwoofer should not be noticeable as being a source of the bass, meaning that it is subtle and definitely felt and heard, but not pronounced as a sound source.

A good subwoofer will support all the other frequencies . . . and they, in turn, will do the same to the lowest bass notes, which can be attested in a balanced system where the subwoofer is turned off . . . and then back on -- the difference is most palpable and fulfilling in its supplementing the sound of the main speakers.

A good example would be a good grand piano. The soundboard resonant the harmonics as do the strings and the cabinetry. What you don't want from you subwoofers are the standing waves that excite the room into a boominess, and a sort of one-note wonder that emphasize certain frequencies in the deep bass. The subwoofer should be capable of singing and playing a bass melody . . . not just a stangnent rumble or irritating thunder for the sake of room shaking bass. To me, it is the qualty of the bass, the solidarity of the sound that give a very satisfying feel and completeness to the overall presentation of the music.

Yes...not that difficult folks.  REL gives a very musical result.  Move it around till you hear best bass integration.  Try even with plane of speaker mid/bass drivers facing parallel or horizontal.