Yes, then ofcourse you would. At least one of my characters was such and as soon as they came to Jarl's houses they would get a housecarl. Unless in Falkreath you assassinated Sidgier's housecarl. He doesn't like you anymore and you don't get an option to buy a plot of land and I don't think you get Rayya either then. Funny, I swear that in a guide they suggested that the Jarl himself could have called that contract, since his housecarl was a bit dissagreeing with his policies. Also, I managed to do it without getting caught. I snuck in there at night and killed the housecarl of a Jarl in his sleep and left before anyone noticed anything. Yet Sidgir started calling my character "misserable wreth" ever since. So all my first character have in Falkreath is blade of Falkreath (which is Dwarven Greatsword) and a title of thane whithout anything else. Although, I happen to have an earlier save of his that I kept, he got all properties there, but in that one he is a follower of Namira, lol Yes that's why I made another save, the file that I used mostly was the one where he killed all Namira followers as warewolf and saved the priest, the other was where he joined them.