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I think Mitaka's actions are mostly moves in the Kyoko game. He's being half-truthful with Kozue, but he certainly says nothing to clue her in on Godai's true feelings. He creates for Kozue a picture of Godai as the gun-shy suitor; to sure up the believability of this creation, he tells Kozue that he himself is too scared to make his feelings obvious to Kyoko, which is a pretty blatant lie. He's already played his aggressive hand at this point, like in the chapter where they go to the festival and he corners Kyoko in the field. However, he knows that if Kozue thinks a suave guy like him has trouble expressing his feelings, she'll have another plausible explanation for why Godai isn't very effusive with her, besides the correct one.
I don't know if Mitaka really has any insight into how Godai feels, and I don't think he really cares. He just wants to keep Godai and Kozue together, and he doesn't seem to feel bad about telling half-truths to accomplish that. I think his defense is that he thinks as highly of Godai as Godai does of him - they both seem to think the other one is basically worthless.
By the end of the chapter Mitaka's pretty sick of Kozue; he gets the results he wants with her, but she bugs him quite a bit in the process. I'm not sure he ever views Kozue as much more than a curiosity, a possible helping hand in his quest to get Godai out of the picture, but also a frustrating one.