It wouldn't be a non-fiction account per se in that it would be a retelling told from the standpoint of "controlled imagination" (i.e. visualizing what it must have been like, what the real people might have thought and felt where there is no record of it, etc.) In sum, it would be the truth about the Titanic re-created like nothing else.
I don't see why a very engaging novel couldn't be constructed this way, but it would be a real undertaking. As a writer and editor, I can say that it would take exactly the RIGHT writer, not just any novelist. There are not many people with the right background to construct a historically accurate account of anything - the example would be the two sequels to "Gone With the Wind," both of which are inaccurate in texture, if not facts.
One problem in constructing a novel about RMS Titanic would be that many people hold some outlandish misconceptions about the ship. You know the kind I mean - the ones who think the ship's decors rivalled Versailles, that the hold was full of gold bars, Rolls-Royces and J.J. Astor's private railroad car, that complimentary jeroboams of Bollinger were provided for the purpose of brushing one's teeth, and that a breakfast of caviar and partridges was served in bed. I have no doubt that some of these people think Caledon Hockley in the Cameron film would have picked up the Heart of the Ocean in a Titanic gift shop.
In fact, the Cameron film - for all its attempts at accuracy - has some stellar examples of textural problems, written into the script by someone who had not the faintest idea that people behaved very differently in 1912, let alone that the differences were there for good and sufficient reason. Very few young women of Rose's purported background would have had a dalliance in the back seat of a Renault at that time, for the simple reason there was no birth control and the woman would have been ruined had a pregnancy resulted. 1912 society had some very blunt, very ugly words for children born out of wedlock, and the people who produced them! Rose's knowledge that Jack had been around prostitutes in Paris would have been another excellent reason for her to have had no horizontal dealings with the young man - prostitutes were widely known as a vector for STDs, none of which were curable at the time. Cameron's adamant refusal to deal with the historical facts concerning the segregation of Third Class passengers from the rest of the ship is another example; it was just too tempting to bring Jack into First Class, thereby advancing his story.
Avoiding hints of 21st-Century manners and mores - as well as getting Titanic's own facts straight - would be a job. It could be done, but not by just anyone. In fact, not by many a writer who might otherwise be very good.