For someone who wrote very autobiographical novels to the point of receiving death threats for his Look Homeward, Angel, I wonder whether he wrote a diary. Did he? If so, does it contradict any of his novels significantly?
According to Wolfe's birthplace, he kept a journal during long trips (Europe in 1924 and the Western US in 1938, his last work). The same page claims, "He once said the reason he wrote a book was to forget it." Wolfe is widely quoted as saying, “The reason a writer writes a book is to forget a book and the reason a reader reads one is to remember it.”
If he kept a journal only during certain periods, we can infer that he did not keep a journal during the other periods. If he wrote to forget, he certainly wouldn't want to keep a diary as a reminder. From what I know of his writing habits, he wouldn't have time for a diary.
There is no way to prove he didn't keep a diary, but I believe these are good reasons to think so.