That's a really tough one to answer!
Logic would say no, they cannot carry out the extension to the rear as an exempt developmnet unless the area of the extension to the rear (built as an exempt development) plus the area of extension (as granted permission) is = or < 40.0m.sq.
However the timing you suggest is curious! Somebody has thought this through whether trying to be devious or not? Sounds like it.
There could be planning compliance issues? They have secured planning permission for an extension to the side of the house on the basis of the area of the existing house being area X. Between being granted planning permission and carrying out that development they add area Y (as an exempt development). Then they go and build development as granted being area Z. Original planning permission was on the basis of X + Z. There has to be planning compliance issues somewhere in all of that?
If it is something that concerns of affects you, I would contact the Enforcement Section of the Local Authority and ask them to investigate.