As I understand it, a player with a game ban on their profile cannot join an EAC-enabled server. Does Steam Checks bypass EAC? So a SteamChecks-whitelisted (but gamebanned) player would be able to join an EAC-enabled server?

This doesn't bypass any checks, it checks what Steam provides after a player has connected to the server.

OK then in that case I'm confused about why this plugin has a configuration to set the number of game bans allowed, when EAC won't allow gamebanned players to join in the first place.

The plugin can check for what Steam provides via its API, and kick the player if desired. Those game bans pertain to other games, not Rust.

Thanks, that makes sense now :)