Karl is one of the Legion's frumentarii, whose duty is to scout the wastes and make contact with tribes that may be able to help further Caesar's cause. He is currently stationed at Red Rock Canyon working as an ambassador of the Legion to the Great Khans. He can be tricked into talking negatively about the Great Khans, which will then lead to his death. His journal is located in a footlocker in his room at the Great Khan longhouse.
If the Courier kills Karl, the Khans will not become hostile. They will, however, receive infamy with Caesar's Legion. It does not seem possible to discredit him with either Regis or Papa Khan if you do so.
Interestingly, Karl pronounces the word Caesar with a hard C sound sometimes when approached (Kai-sar) but pronounces it with a soft C (Seize-er) in most of his text. This is most likely an error of taking a generic legion text file, and applying it to a unique non-player character of the same voice actor. His English pronunciation of the word is more like everybody else who isn't affiliated with the Legion, despite being a member of it. The same glitch/quirk can be heard in the dialogue file of the Legionary guarding the weather station at Fortification Hill, who is voiced by the same actor.
Karl also seems to have an honorable view of the Burned Man while most members of the Legion despise him.
If the Courier kills Caesar, Karl will angrily threaten him/her, saying that he would avenge Caesar if they weren't on Great Khan soil. In some cases, he may attack on sight, but the Great Khans won't intervene for the Courier or Karl.
Karl will remain at Red Rock Canyon even if the Courier has already killed all the Great Khan inhabitants.
Halfway through the quest Oh My Papa, Legionary assassins will attack the Courier saying that "Karl sends his regards". If they are defeated, Karl himself will appear a few days later and attack the player character after initiating dialogue.
If Karl is killed, his footlocker in his room (inside the longhouse) can be looted freely with no loss of Karma.
Even if the player character is vilified with the Legion, he won't be hostile on sight but still say that the Courier is perilously close to making an enemy of Caesar, even if Caesar is dead.