Diamonds actually get their value because a single entity (DeBeers) owns something like 80% of all diamonds in the market.
They dictate the price by throttling supply and naming a price. People are willing to pay as a flex but you are right in that DeBeers markets "real" diamonds and "lab grown".
It's mostly done to capture different market segments, and to keep up the value of their stockpile of nearly unlimited diamonds already mined by people who are essentially slaves.
That being said, if there was a market for diamonds soaking in vials of oppressed orphan blood (with provenance of course) DeBeers would absolutely sell it.
If lab grown diamonds became significantly cheaper than slave mined diamonds, DeBeers would still likely keep their mines open to maintain control of the market. Even if they successfully moved consumers on to lab diamonds - can't have someone else get diamond market share.
There was a study done a while back that looked at what happens when fake contraband (rhino horn in this case) is mixed in with real ones. They found that killing of rhinos went up because people wanted the real horn. The goal of pushing out fakes was to decrease the demand and it ended up with the opposite effect.
I imagine that diamonds will be similar.
Until there comes a point where anyone can grow a diamond in their home, DeBeers is going to continue to exploit people.
It is impossible to tell natural from man made diamonds. If it becomes cheaper to make them then EvilCorp will switch to doing that and probably not tell anyone.