Yes, Titanic did send out distress messages via Morse Code. The station log went down with the ship. But the communication has been reconstructed from other written logs. They show that Titanic didn't use SOS.
Next week is the 100th anniversary since Titanic sank on April 15th 2012. Thanks to Lou Josephs for finding a very interesting web page (and it is a single page!) with a collection of photos all about the communications on board the ship. The fan page includes the transcript of the last known communications from the ship where it seems that the operators used the CQD (Calling all ships) phrase in Morse rather than SOS. It had been introduced by the Marconi company, but wasn't in common use in 1912. Fascinating piece of work. It would be great if it's integrated into the Wikipedia page. Seems the coordinates the ship was transmitting turned out to be a bit off. The wreck was eventually located 21.2 km away from the position reported by the Titanic crew during those Morse Code exchanges.
Noticed on the Tube train last week that Belfast is commemorating the shipyard where Titanic was built in a rather spectacular way. Surprised that the Northern Ireland Tourist Board didn't make a special landing page for this. When I typed the URL on the ad, I didn't see anything about the Titanic and had to search.