Being a long-time navy guy still on the coast, and as someone who has completed his AJOSQ, and is waiting to do the ATOC - I can state that the Navy does not have anything like AJOSQ.
That said, I doubt there would be a benefit for it. Outide of a few of the modules, I doubt that even the army people see much benefit to AJOSQ. From what I've heard, ATOC is a bit better, and AOC is supposed to get good from a learning point of view.