That can work, not as a way for Sirius to survive, but as a reason for faking the death of Sirius and/or Dumbledore. In the minds of the characters, this could be a motivator for Harry. It did motivate him to chase Bella out into the atrium, which was fool-hardy. But after that, it just left him depressed.

Three problems:
(1) They both know that Harry is already motivated.
(2) They both know that Harry has suffered enough.

(3) I think JKR had a reason for killing Sirius.
I have felt for a long time that JKR's true purpose in bringing Sirius into the story was to make him lovable and then kill him off. This idea started nudging its way into my mind at the end of the fifth book, but I pushed it away. She made him too lovable. But plot-wise, she made him expendable. I hate to say it, but Sirius doesn't really have a role in the main plot. Like Harry, I didn't believe at first that Sirius was gone. But by the end of the fifth book, I was satisfied. Search your feelings, Luke. I didn't like it, but it felt true.

My vague thought goes like this:
She killed off Cedric, a lovable but minor character, to wake us up to the idea that people can die.
Then she killed of Sirius, a lovable, major, but expendable character, to drive the point home.
She's set us up, and now expects us to believe that she would kill Dumbledore.
Nope. I'm not buying it.