Besides, if Khan's blood brought back the Tribble (as McCoy said, his blood has regenerative capabilities beyond anything he'd seen before) it is possible that it would save a 'slightly dead' Kirk. A dubious possibility, but a possibility nonetheless.
Yes, but the point is WHY McCoy decided to inject the tribble with the blood in the first place. Having McCoy research Khan / Harrison and finding some link between him and the girl at the start would have been reason enough. It would have been a logical progression of the story thread and
would have given McCoy something to do, besides getting his arm trapped in a torpedo.