Yes, I may not know the exact value of my utility since I don't know the value of every argument it takes, and yes, there are consequently changes in utility which aren't accompanied with corresponding changes in happiness, but no, this doesn't mean that utility and happiness aren't correlated. Your comment would be a valid objection to relevance of my original question only if happiness and utility were strictly isolated and independent of each other, which, for most people, isn't the case.

Also, this whole issue could be sidestepped if the utility function of the first agent had the utility of the second agent as argument directly, without the intermediation of happiness. I am not sure, however, whether standard utilitarianism allows caring about other agent's utilities.