They'd have to pull a complete switcheroo, like saying that Actor X had been cast as the new assistant and would appear mid-season. Then without warning kill of the 11th Doctor and have him suddenly regenerate in Actor X. But you'd have to keep the casting process known to a tiny group of people and shoot the scene to a skeleton crew. I think it would be simply impossible to guard against the news getting out somehow.
And, honestly, why would you want to do this? A New Doctor generates interest. It generates higher viewing numbers. Why would you want to keep it a secret? Why would you NOT want as many eyes in front of your program for your big event? Because it would satisfy a story point? Because it would surprise a few people? (Obviously not a few, but, still...)
To not advertise the big event that happens every few years in Doctor Who would be silly.