They did have armoured trains (one fought a very one sided and terminally short engagement with a British warship at the Dardenelles).
They had more than one armoured train. I believe that they used some on the Damascus Medina line (the one Lawrence blew up was not armoured, no armoured train ever got as far as his sphere of operations thanks to the efforts of irregular forces under Col Leishmann operating much closer to Damasus - funny Lawrence never mentions this (not))
There is a photo of Enver standing by an amoured car with some members of the Young Turk movement seeking to overthrow the Sultan.
The Turkish army seems to have been a mixture of old and new - virtually no mechanised transport but a better understanding of the use of heavy machine guns (and the guns to implement this) than did many other armies of 1914.