Nerd, read carefully because I will say zis only once. Presumably you are talking about the foremast. The cargo derrick was hinged at its base and did indeed 'fold' back against the mast when not in use. As it wasn't deployed at sea and wasn't used at Southampton either its presence is not immediately obvious but can be clearly seen in photos.
Not sure, but I think you'll find that all the derricks fitted to Titanic had a facility for stowing them horizontal on a thing called a 'crutch'. Vertically stowed derricks was an American idea. Back in my day we could tell a 'yank' ship miles away by the ay her derricks were stowed. Vertical stowage could cause a stability problem as well as a horror story if one broke loose in a storm.