My understanding of Lumen is total light output measured from a light source, be it single or cluster. Using that definition I would say yes, Lumens is cumulative. I believe this is the value most suppliers will use for their products, as it is easier to draw a direct comparison across the board. So in the example previously given, 3x200L's would be the equivalent of a 1x600L, using that definition.
If you are talking about End Lumens, that is a different measurement, and is dependant on many factors such as those previously mentioned IE, lenses, reflectors, source convergence, surroundings..etc. All those variables could increase or decrease the total end lumens depending on design and set up.