@Livingtothefull just looked Murdoch up on Wikipedia:
Death
Edit
Several eyewitnesses, including Third Class Passenger Eugene Daly and First Class passenger George Rheims, claimed to have seen one of the ship's officers shoot one or two men during a rush for a lifeboat, then shoot himself.[17] It became widely rumoured that Murdoch was the officer.[17]
In a letter to Murdoch's widow, Second Officer Lightoller denied the rumours, writing that he saw Murdoch working to free Collapsible A when he was swept into the sea by the wave washing over the boat deck.[18] However, Lightoller's testimony at the U.S inquiry suggests that he was not in a position to witness Murdoch being swept into the sea. It is also possible that Lightoller may have wanted to conceal the suicide, if it occurred, from Murdoch's widow. Later in life, and according to a family friend, Lightoller reportedly admitted that someone did die by suicide in the sinking. Additionally, James O. McGiffin, son of Captain James McGiffin (a close personal friend of Murdoch), said that Lightoller had told his father that Murdoch had shot a man.[18]
The allegations of an officer's suicide was portrayed in the 1996 miniseries Titanic and the 1997 film Titanic, both portraying Murdoch as the suicide victim.[17] When Murdoch's nephew Scott saw the film, he objected to the portrayal as damaging to Murdoch's heroic reputation,[19] and film executives later flew to Murdoch's hometown to apologize.[20] The film's director, James Cameron, said that the depiction was not meant to be negative, and added, "I'm not sure you'd find that same sense of responsibility and total devotion to duty today. This guy had half of his lifeboats launched before his counterpart on the port side had even launched one. That says something about character and heroism."[21][22]
Author Tim Maltin (Q119846417) writes that, although the evidence is circumstantial, "it does seem that an officer did shoot himself and Murdoch seems the most likely candidate. As Titanic experts Bill Wormstedt and Tad Fitch point out...Murdoch was the man directly in charge of the ship in the hours leading up to the collision with the iceberg and he was therefore responsible for the ship and all its passengers during that time. His career at sea was effectively over, even if he survived the disaster"
Not exactly conclusive but certainly possible then.