I'm talking about a plugin that kicks a player if their ping is too high/lagging. Does their lagging cause the server to lag more when they're connected or something?
Their lagging does not hurt the server.
Players with high ping usually lag visibly in-game, such as seeming to stutter or 'teleport'. This makes them more difficult to hit as they're not actually where they appear to be, giving a bad experience for the other players.