Sorry, I spend a large amount of time standing on the concourse most days, I am very much positive that they do not do what you mention any more. There was a period about 2 years ago or so when it was tested, but it was stopped for reasons I don’t know.
Sorry, but I happened to work on this bit of railway, and I reckon I spend rather longer at the station than you do. The concourse board information does not necessarily catch up with delays, which means the train will still show on the board at its expected departure time, marked with "On time" beside it. But almost every time I have seen a train still displayed on the boards at its scheduled departure time, I have headed in quite a leisurely way to the platforms, and found it to be slightly delayed and only just arriving. If it doesn't do that, this is, as I say, a technical fault.
An example is the xx48 evening departures towards the South Coast via Horsham. For historic pathing reasons, these trains often lose at least a couple of minutes around East Croydon. Often the departure boards will show they are On time at xx48, and yet they are still back at Windmill Bridge Junction, having been on time when they arrived at the previous point at which the system tracks them (Selhurst Station). You can walk down the ramp quite comfortably and see the train pull in as you get to the bottom. Admittedly you then have to fight a bit of a surge of people leaving the front of the train, but it's no worse than the usual peak scrum, plus you are in full view of the dispatcher by the dispatch equipment box.
Obviously all station CIS has to remove trains from the boards at some point, but the timing varies per the size of the station. There is absolutely no point in displaying trains on the East Croydon concourse which have already arrived, as people will be likely to miss them even if they run.