Does LOD work on models that are part of a map entity?

I haven't explictely tested it, but see no reason why it shouldn't work.

One way is to just run a small experiment. Build a map entity and check the frame rate. Build all the models separately without LOD used and check the frame rate. Build all the models with LOD and check the frame rate. Finally, put the LOD entities into the map entity and check the frame rate. If the frame rate increases on the last step, LOD is being used. Of course, you may want to test some variants of this to help ensure that. It's the best approach - use the scientific method for running an experiment.