Sorry, I should have explained a bit further. I am referring to biodiversity as the 'macro' creatures which live in the rock. For example, snails, crabs, starfish, pods, chitons... the list goes on and on; some good, some not so good. These things may or may not reproduce, thus the 'biodiversity' may not extend to the other rocks in the tank.
The dry rock will 'cycle' within a couple months to be able to process the 'input' into the tank (including food, critter waste, dead things, etc). It will normalize and balance itself out in a matter of months. However, if suddenly your auto-feeder falls in the tank, or a large critter dies, you could see ammonia and nitrite spikes due to the nitrifying bacteria not being able to process the sudden shift in 'input'. Hopefully that makes sense.
So, to answer your question, yes, I would consider rock which has been in a functional aquarium for two years to be live.