Does the story of Koch have any effect on Raskolnikov?

Yes, the story of Koch had an effect on Raskolnikov. It is this story that makes him realize that there are people who believe the murderer has not been found, and that there are also people prepared to defend the accused.

"And then Dmitri escaped and ran into the street, and I ran after him; but I did not catch him, and went back to the flat alone; I had to clear up my things. I began putting them together, expecting Dmitri to come, and there in the passage, in the corner by the door, I stepped on the box. I saw it lying there wrapped up in paper. I took off the paper, and saw some little hooks, undid them, and in the box were the ear-rings.…’ ” 54

“Behind the door? Lying behind the door? Behind the door?” Raskolnikov cried suddenly, staring with a blank look of terror at Razumihin, and slowly sat up on the sofa, leaning on his hand. 55

“Yes … why? What’s the matter? What’s wrong?” Razumihin, too, got up from his seat. 56

“Nothing,” Raskolnikov answered faintly, turning to the wall. All were silent for a while. 57"

“How do I explain them? What is there to explain? It’s clear. At any rate, the direction in which explanation is to be sought is clear, and the jewel-case points to it. The real murderer dropped these ear-rings. The murderer was upstairs, looked in, when Koch and Pestryakov knocked at the door. Koch, like an ass, did not stay at the door; so the murderer popped out and ran down, too, for he had no other way of escape. He hid from Koch, Pestryakov and the porter in the flat when Nikolay and Dmitri had just run out of it. He stopped there while the porter and others were going upstairs, waited till they were out of hearing, and then went calmly downstairs at the very minute when Dmitri and Nikolay ran out into the street and there was no one in the entry; possibly he was seen, but not noticed. There are lots of people going in and out. He must have dropped the ear-rings out of his pocket when he stood behind the door, and did not notice he dropped them, because he had other things to think of. The jewel-case is a conclusive proof that he did stand there …. That’s how I explain it.”

I do not believe Koch's statement effected Raskolnikov. The novel is about his struggle of proving to himself that he is an "extraordinary" member of society able to transgress moral law. Obviously he never was and no one is able to transgress moral law. Raskolnikov would have felt his guilt anf fear of imprisonment regardless of Koch's testimony because he is not superior. If anything, Koch may have increased the omnipresent fear within Raskolnikov of beinf mediocre, but there was no real importance.