That would be difficult as the RMS Titanic sank on its maiden voyage across the Atlantic in 1912. It also had four funnels, not three. The ship depicted in the episode was the RMS Queen Mary, apparently, which didn't start operating until 1936.
IIRC, DW has never done a Titanic story on screen if we don't count Voyage of the Damned. John Hart and Jack Harkness were on board according to one of the Torchwood audio stories. The Time Machine travellers Doug Phillips and Tony Newman were apparently also on board but didn't get it on like the other two.