Welcome to the website,
You may find that sway bars can improve somewhat your cornering ability but not sure how much they will improve things since you have the "soft ride" LTZ suspension components on your AV. That model is supposed to give you a soft smooth Cadillac type ride and auto adjust for loads and towing etc. It is not designed for performance handling.
If you want to convert to a performance handling type setup you may be opening up a can of worms and end up buying performance shocks, springs,bushings etc. There is some sensor issues if you do decide to remove the LTZ air shock system and go for a more standard shock FYI.
You may find some info in the suspension mod/performance sections for the sway bars though.