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

Hey Sparky, I’ve owned Wilson 6’s, 7’s, Dynaudio C4’s, B&W 802D3’s etc and Reference hear from ARC, Levinson, Krell etc..  Been there and done the whole no sub thing.  Short of those types of systems and great rooms (insert plga) a sub adds texture, spaciousness and warmth.  It is not to blast more bass.  Adding room correction electronics to a system, IMO adds extra artifacts and strays from the original musical content.  Talk about using a computer to deal with a problem an abacus could solve...jeez!  Placing a sub is hard if your hard of hearing.

It doesn't take an engineering degree Larry but a little time spent learning a little about each of the areas involved sure does help.

Like, sound travels in waves. The lower the frequency the longer the wave length. This one simple fact seems to cause a lot of problems though because it means sound in a room behaves quite a bit different than most people think. What I mean is most people think it all behaves the same. In fact it behaves very differently depending on frequency. Not only does it behave differently, but we even hear it differently!

Its real easy to get confused by people who don't know what's going on, get their facts wrong, and talk about things like toe in and timing which do matter from midrange on up but do not matter at all at low bass frequencies.

If you want to understand there's great articles already mentioned above by Geddes and O'Toole, and of course everything posted by audiokinesis on here is pure gold. Everything else you should take with a big grain of salt. What is not flat out false is maybe even more dangerous for misleading with a grain of truth. There's also a book I can't recommend enough The Complete Guide to High-End Audio by Robert Harley.

As an example of a little knowledge.... plga has a room 14x28x9 which just that one thing is enough to know he's gonna have problems with a sub. Why? Because 28 is exactly twice 14 and almost exactly three times 9. This means nodes are gonna stack up at 40Hz and 80Hz. Why? Because at 40Hz the wave is 28 feet, at 80 Hz 14, and at 125Hz 9ft, and 125 is almost exactly three times 40. You could literally take a piece of graph paper and map out the nodes and see them.

No wonder plga has had so many problems. He's trying to solve a problem of physics the wrong way, with a sub. The key word being "a".

Now look at noble100. His room at 16x23x8 is almost as bad yet he is really happy with great sota bass! Partly this is because the larger dimensions (16, 23) aren't multiples so troublesome bass nodes are further apart. Mostly though this is because Tim has wisely chosen to solve his bass problem with an actual, bona fide proven to work solution- a distributed bass array.

A little knowledge does indeed go a very long way.

Years ago I listened to a pair of magnepans at a dealer and the subwoofer was located a few feet behind the listening spot.  It was the first time I’ve experienced expanded height to a soundstage. When they turned the sub off, the stage seemed to collapse back down.  I don’t hear a lot of people with this type of placement as it usually seems to be more toward the front of the room near the mains.

Hey Dave. 
Take it easy.
Im only telling my experience. I dont doubt about yours as you mention you seem to have much with very popular brands, but that doesnt make mine not valid. 
Im also aware that my room dimensiones are difficult as posted by millercarbon (thanks for pointing that out), but I cannot change them. As I said YMMV. 
I also have to say that I would LOVE to hear a high end system improved by subs as I cannot imagine it with out hearing it. 
Anyway, I still think that getting the best system your budget can afford and voicing it to the room should be the first step and then, with that experience on your back, if you are not happy or totally satisfied with the results, you should get with subs. 

All good!  Experimenting is fun...enjoy and happy listening.