I absolutely would have read it. I agree with the quote his brother Charlie used to justify it: "No one knowingly chooses to live without the truth." And as Iris points out, in her post above, Placidia was deceased, and had been for some time. Violating her privacy was not a compelling argument against her son's desire and perhaps his right to know the truth. (So Iris, I don't think you have a double standard there at all, but an important distinction between seeking valuable knowledge and prying.)
I did not fully understand at first why reading the diary caused him to break off with Roe, but once I read that part of her diary, I can also appreciate his feeling that it gave him a deeper understanding of what a true bond between partners can be, and realize he needed more life experience before making that kind of commitment himself. The truth may not make us happy, and we can't unlearn what we would rather not know, but we can grow in wisdom and gain from truth in the long run.