SWT definitely used to when I commuted with them in the late-2000s.
The 8.36 Guildford to Waterloo stopper via Cobham doesn't have any scrolling message about first class being declassified. Well not that I've noticed. There again I don't sit in standard class on that service.
Clearly most people are unaware as the rest of the trains fills up more quickly than the declassified first class. At the journey goes on you get more people sitting in first class but it's never totally full. These will be regular commuters in the know.
Similar occurs when I board the 17.11 from Surbiton (starts Guildford at 16.37).
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Inverness allocated class 158's (701-725) have a First Class area. This is only used on Inverness to Aberdeen or Inverness to the South. When these units are on Far North duties, First Class is de-classifed and the train is fully standard class. As the First Class seats are the only ones with charging points, they get filled up pretty quickly by the laptop brigade.
That's precisely why I sit in First class when it's declassified. I can charge my mobile. I also like table seats.
If the 450 stock had table seats and charging points in standard class, as the 444 does, I would sit their just as happily as I would in first class.