Modes and modal (and non-modal) ringing occur in EVERY room - not just square ones. And yes, you should worry about them.
In reality, a square room is not ideal. There are some people who think they would prefer a square room. As the logic goes, in a square room, all the modal issues are together and should in theory be easier to treat. Unfortunately that's poor logic.
Having a rectangular space allows the modes not only to be spread out, but in doing so, reduces the intensity instead of having spots where you have literally double the intensity of peak or null.
Now that the theory is over, you still have a square room. As Ethan said, 20x20 is better than 10x10 and you can certainly get some good sound. You'll need to do the same things that everyone else does.
- control the bottom end
- control early reflections
- treat appropriately to bring the room into an EVEN decay time targeted based on volume and usage
What you will need to do over and above is:
- be even MORE concerned about seating locations as there will be a few places that WILL have overlapping modal issues
- potentially think about some targeted (tuned) treatments for more stubborn issues
- almost definitely plan for parametric EQ on the subwoofer.
Welcome to the madness....
Bryan