Given the fact that Ant and Dec, Graham Norton, The Last Leg etc have all mentioned the studios closing down, it is so obvious they are moving out, so I guess they will mention it on the first day and that is it. If This Morning and GMB want to use the outdoor look of Television Centre as they did often on the Southbank, then it will become even more noticeable where they are at, they can't hide any pretence.
But there's a major difference between those shows and This Morning. Those shows have indeed mentioned it but the aspect of the South Bank itself plays no element whatsoever in the show really. They could be held in any studio and no one would be none the wiser - yes, Ant and Dec have used the building from time to time and on the titles, but the majority of the show is from Studio 1. This Morning however has the view of South Bank as a major element of the programme... it's always there on show because it's part of the set and the windows have always been a big part of the show. That's why I'm unsure whether they'll mention it. If they do opt for outdoor segments, then, yes indeed it might shatter the illusion. However, most non-TV enthusiasts will just think that they're in a yard/garden somewhere and not at
TVC. Indeed, if they do spot that they're using somewhere at TVC, many viewers that don't have any awareness of London might just think that TVC must be right next to the South Bank! We sometimes forget how unknowledgeable the average viewer is.
Another thing to consider is that it's only been in recent years that they've used the South Bank a lot more - when This Morning moved there originally, they sometimes went outside but not as much as they tend to now and many segments were indoors. It might simply be a case of going back to basics more - they've got a bigger space to play with so they might actually find it easier to create small temporary sets for certain segments or record segments on location somewhere.
I can see there being a mention of moving studios at the end of the final show, but I do wonder whether they'll mention moving away from South Bank so the average viewer just thinks they're in another one with a view of the Thames. These are all just thoughts though and a huge assumption that the fake windows will display a view of the Thames. It could be a recorded shot of Westfield or Hammersmith Park with some ducks on the pond yet.