Certainly. But that is a different kind of trauma and in a situation like with the Titanic, unlikely to lead to 'conventional' PTSD (if there is such a thing).The only thing I could add is that I've read accounts from survivors that have said listening to the screams and cries of the 1500+ people in the water never went away. It stayed with them their whole lives.
Also, one has to bear in mind that Fleet was rescued on Lifeboat #6, with QM Hichens in charge. If other survivor accounts are to be believed, he declined to go back anywhere near the sinking ship and by inference, might have been too far away to hear the screams and other sounds towards the end. But I'd like to be enlightened on this; did many survivors on board Lifeboat #6 report hearing them?