The Virginia biologist who is tasked with studying them and documenting any effect of their presence has stated they are not having any negative impact. This includes largemouth. I've known this for a while as many places I catch snakeheads the largemouth fishing has gotten better. The largemouth love snakehead fry conversely snakeheads are eating few largemouth. They primarily eat killies and bluegill.
https://www.youtube.com/watch?v=djvayxqjrfQ