Ramen is often made with kansui, which is an alkaline solution that brings the pH of ramen up to 9-10. The noodles themselves are 6-7, ramen made without kansui but a still salty traditional broth will be around 8-9.

The pH of listerine and orange juice are both around 3, so the clash of their flavors is accentuated by their acidity. Listerine + ramen with kansui would probably just taste like a little bit of a minty tang, but relatively smooth since the pH would balance out. Probably wouldn't be all that bad.

Note, I'm no ramenologist, I just Googled some shit