To answer the original question: I think it is believable that Oskar would be ready to kill and kill again in order to be with Eli. I don't really see Karin or Stefan being ready to spend years, months, decades, (centuries?) draining blood form innocent persons (even if they don't yet know about the neck-breaking thing yet). In the LDKRI, John lays a lot of ground work to support the idea that Oskar could be capable of living the life of an infected. The first time he meets Eli, as he is stabbing the tree:
There was enough light for him to determine that it was a girl he had never seen before. Oskar took a step toward the jungle gym. The girl didn't move, just stood there looking at him.
He took another step and suddenly he grew scared. Of what? Of himself. He was on his way toward the girl with his hand tightly closed around the knife, on his way to stab her with it. No, that wasn't true. But that was how he had felt, for a moment. Wasn't she scared?
Among other things, that passage shows a link between Oskar's rage and his violent fantasies, and then goes on to hint that his fantasies could be ready to leak into his reality. Then after getting whipped in the school yard, Oskar creeps himself out talking to himself in the mirror and has a very detailed fantasy about killing Tomas:
He took the rinsed Pissball and put it on his nose. Like a clown nose. The yellow ball and the red wound on his cheek. Oskar. He opened his eyes wide and tried to look crazy. Yes. Creepy. He talked to the clown in the mirror.
"It's over now, it's enough. Understand? This is it."
The clown didn't answer.
"I'm not standing for this. Not even one more time, understand?"
Oskar's voice echoed in the empty bathroom.
"What should I do? What should I do, do you think?"
He twisted his face into a grimace until it hurt, distorted his voice by making it as raspy and low as he could. The clown spoke.
"... kill them ... kill them ... kill them."
Oskar shivered. This was a little creepy for real. It really sounded like someone else's voice, and the face in the mirror wasn't his own. He took the Pissball from his nose, put it back in his pants.
Not because he really believed in this and all ... but he would go stab the tree. Maybe, just maybe. If he really concentrated, then ...
Oskar picked up his bag and hurried home, filling his head with lovely images.
Tomas is sitting at his computer when he feels the first stab. Doesn't understand where it is coming from. Staggers out into the kitchen with the blood gushing from his stomach. "Mom, Mom, someone is stabbing me."
Tomas' mom would just stand there. Tomas' mom who always took his side no matter what he had done. She would just stand there. Terror stricken. While the stabs continued to puncture Tomas' body.
He falls to the kitchen floor in a pool of blood, "Mom ... Mom while the invisible knife cuts open his stomach so his intestines spill out onto the linoleum.
Not that it really worked that way.
The passage above definitely paints a picture of Oskar's inner pent up rage making him comfortable with the idea of killing. Now Oskar's anger is urging his conscious mind to act with violence, and he is showing signs of being able to dissociate himself from it.
Then when Oskar thinks he is going to become infected because he handled Eli's bloody clothes with his hand that the cut on it:
I'll help you.
He looked at his hand again. The hand that helped. The hand that ...
I'll kill someone. I'll go in and get the knife and then I'll go out and kill someone. Jonny. I'll slit his throat and gather up his blood and then I'll bring it home for Eli because what does it matter now that I'm infected and soon I will ...
His legs wanted to crumple up under him and he had to lean on the edge of the garbage chute not to fall over. He had thought it. For real. This wasn't like the game with the tree. He had ... for a moment ... really thought about doing it.
Now here, finally, Oskar's rage at Jonny becomes coupled with Eli's survival. Now his revenge on his tormentors can be coupled with some higher cause, and for a second this seemed a good idea to Oskar. JAL spends time taking on this journey of showing us how Oskar not only accepts that Eli kills to survive, but could be ready to take part in it. After the foundation laid in LDKRI, it does not seem surprising that by the time Oskar reached Karlstad in LTODD he would be ready to take on a life of killing in order to be with Eli.
However, with Stefan and Karin, I don't think any similar foundation has been laid. Yes, they would most assuredly be ready to spend eternity with each other, but the killing? Is there anything in LTODD that would make us think that either of them would be ready to take part in even one killing, let alone hundreds or thousands? Being twelve, Oskar can probably not think too far beyond today. He could not imagine a trail of murders stretching unbroken into the indefinite future in order to keep himself alive. As an adult, Stefan would be able to visualize this consideration, and as a former Blackeberg police officer Karin would have first hand knowledge of the cost of such a choice. I can't see either of them even asking to become infected, let alone actually following through on such a choice.
In a way, they are avatars for most of us here: They are willing to toss everything aside for a chance to meet Oskar and Eli, but that doesn't mean that they want to be
Oskar and Eli. Which of us would not buy a plane ticket to Spain (if at all possible) in such a situation? Would that mean that we want become infected?
Just as I thought that LDKRI didn't need to continue beyond Oskar & Eli together on the train, so I also think that the story of Karin & Stefan doesn't need to continue beyond them possibly meeting Oskar & Eli. I think LTODD offers even less guidance about what becomes of K&S than LDKRI offered about O&E, and I kinda like it that way.