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

Yes, a sub makes a positive difference. Best to check it out in your own home to see if it’s worth the money. Read into the MartinLogan Dynamo 800x. It’s a bit more than $500. Features Anthem room correction and tons of other settings. This way from your app you can blend the sub and fine tune every setting. This is a good situation if you are running a 2 channel rig without room correction. It’s a compact sealed design. Super fast and punchy. Many online retailers offer generous exchange policy. Ultimately the in home trial is the only way to be sure. Good luck and great question.

I am convinced that adding a pair of subs 
1. Improves the bass range
2. Cleans up the midrange 
3. Widens the sound stage .
the key being placement and tuning ie the phase setting and volume of subs.
i use my pair of kef blade 2s along with a pair of Jl Audio f113 v2. The sound improvements after adding the subs were phenomenal through the entire spectrum.
i am not a profound supporter of room sound correction programs .
noble100 was right on the dot till recommendations no 5, from that point on I tend to differ from him. Not saying he is wrong but saying his techniques are different .
i would recommend you contact Barry Oder ie the sound doctor. His experience with subs spans over 4 decades. I spent a weekend with him and learnt a lot which I have used for setting up my sound . If you call Jl Audio for help they would guide you to the white papers written by Barry . He is a true guru .
http://www.soundoctor.com/whitepapers/subs.htm
Read the above paper written by him and you can contact him over phone . He is a tremendous resource and loves to help people who love bass. Who doesn’t . 
You don’t need a Jl Audio sub to make great music but you need to have it perfectly aligned with your main speakers to sound great .time domain is in my opinion crucial . 

Only way to know is to add a sub. I’ve always found it to be complimentary to any system as a sub can make movies really go wow! Not sure about room correction, I move the sub around and tune it constantly until I achieve what I need to integrate it. Sure there will be imperfect moments within certain songs but overall it’s much more fun to listen with a sub.

I would add a pair of REL T/9i's.  I listened to the Focal Aria line and I kept asking myself where is the bass.  I also asked myself if audiophiles do not like bass in general.  Even their largest 948 aria speaker lacked in bass extension.  Adding two T/9i's will really help.  

The best thing about subs is that you don't need them when your speakers are good. And if they are not good - replace them. And don't forget good source, electronics and cables.