What functional programming does mean right now is that it's much easier to chop your program up into reasonable-sized chunks: big enough that it's worth the overhead, small enough that you can distribute as widely as possible.
In other words, if you think of a functional program as a tree and then expect to run each leaf in its own thread, the overhead will vastly outweigh the benefits. But the functional semantics also allow you to run each of the dozen main branches in separate threads with little effort.
I do this in Clojure all the time.