The Wormhole wrote:
Such a thing would not be possible. The departure of a Doctor and casting a new one are pretty big deals. There's no way for the BBC to practically stay silent about it.
be able to get away with it in a season finale, if they don't cast the new one yet. This year, the stars aligned where they could have pulled off the scheduling; the shooting for the Anniversary/Christmas specials could have waited until after the series 7 finale airs and they'd still have plenty of time.
The BBC would truthfully be able to say that Matt Smith's successor has not been cast. Evading Matt Smith's departure is harder, but plausible.