Yes using Listerine to wash your mouth out can kill the bacteria in your mouth that can lead to gingivitis.
It's a good idea to wash your mouth out using Listerine daily at least twice per day to keep your mouth clean and bacteria free and protect your teeth from gum disease and Gingivitis.
You can also use Apple Cider Vinegar to prevent and treat Gum Disease as well as Gingivitis because Apple Cider Vinegar is naturally antibacterial and antiviral that causes it to kill off germs and bacteria in your mouth.
Also be sure to brush your teeth after every meal everyday and floss your teeth as well.