Yes... curious minds can certainly speculate about Harry and the Nawab, to be sure. In any case, I found a blog that describes in detail each major character and their relationship to the other characters:
Of course, this is directed more towards the book than the movie, but still, it gives you an idea of "who's who" in the movie, since the movie tries to follow the book.
Harry is described thusly:
"Harry is an old friend of Douglas, Tessie and Beth. He lives with the Nawab at his palace although he originally comes from Great Britain. His role at palace is not accurately defined. Harry is not very handsome and attractive but he is a great entertainer and knows how to amuse people. Unfortunately, he suffers from the heat in India and does not feel good at hot days. He is torn between staying with the Nawab and visiting his ill mother in England and stays because the Nawab persuades him. So he loves to visit Olivia and he calls her house an oasis. Furthermore, he does not like the relationship between Olivia and the Nawab but helps Olivia when she wants to have an abortion. One day he eventually manages to persuade the Nawab to go home. There he lives several years with his mother until she dies and after that with his friend Ferdie. The Nawab often visits them. He keeps contact to Olivia’s sister Marcia and so he got the letters from Olivia to Marcia written in 1923. After Douglas death he brings the letters to Tessie and Beth."
"Old Thomas Jefferson said that he was a warrior so his son could be a farmer, so that his son could be a poet." — The Missouri Breaks