will adding a subwoofer improve overall audio

"....would a sub help?"

Maybe.............

Depends on the size of your room
Depends on the dimensions of your room......
Depends on the set up you can facilitate......
Depends on what sounds you are trying to add or correct....

A sub could add some bass
A sub could help you with bass problems if properly integrated
A sub could give your main speakers a better sense of 'body'

A sub will not add to your systems clarity - in fact it could cloud it up if not properly integrated......
A sub will not enhance the sense of soundstage - generally speaking that is more a function of mid/high frequencies and set up......

Rives is right - sub integration is neither easy nor cheap if you want really quality results.

FWIW, except to compensate for room problems with full range speakers where you can use sub positioning to help fix it (flatten out nodes/reduce boomyness) I'd always use full range speakers (even small ones) and run them full range and add a sub, rolled off below 60hz, to fill out the bottom end. This can be done, sub wise cheaper and easier because you don't have to deal with the effects of a cheap cross over with the main speakers.

All IMHO, but something for you to consider.

Unless your main speakers are capable of faithful ~20hz reproduction, yes a sub will help. In my experience imaging, and overall accuracy improves no matter the size of the room. A good sub can be tuned to fit, though selecting the sub with the room size in mind is a good idea. IMO it's more important not to have too small a sub, than to have one too large for the room. One that's too large can be attenuated using the volume knob.

In my experience a sub made a tremendous difference. I have large floor standing speakers but my setup is in a corner and the ceilings are lower than most. This is far from ideal but I'm probably not the only one with a less than perfect listening environment. So, I ended up putting subs, passive boxes, in the corner sitting back farther than the towers. They fire in opposite directions and perpendicular to the mains. Having this setup for a couple years I can tell you it is the solution for me. I feel that I have successfully changed the negative characteristics of the room and it really sounds great as a result. The overall sound is much fuller and balanced.

Only if it is a high quality sub, correctly installed and tuned, and matched with the correct speakers. No if one or more of the above are not met. A su is not magic, but has the potential to be. Jallen