No it wasn't. The Stockton & Darlington Railway was opened in 27 September 1825 and carried passengers on the first date. Regular passenger services started in October 1825.
A bit of a 'vague' claim. Cameron claims to have spent more time 'with the ship' than the passengers but he's never actually been on it (it's at about 3,700m down - or 371 ATM - way beyond what any diver could survive). He has dived in a submersible to the ship on a number of occasions but you could only claim he'd spent more time 'at the wreck' than the passengers spent on board if you included the time taken to dive to the wreck and surface again. The actual time spent at the wreck was much less.