If he doesn't get a chance to arrange, say, for messages to be sent out in the event of his death or incapacitation, then his best bet might be to tell them, but if it looks like he can get away with it it might be better for him to imply that he's already told some people, but not reveal who. That way they will conclude they can no longer rely on dementors, but the secret doesn't actually escape.
He did already give Hermione that letter which she could use to find out the secret, but it's probably too late for her to make any use of it. It would have been a good idea for her to read it as soon as she was told that she was accused of murder, except she probably never had the chance to do that, and anyway she won't have a wand in Azkaban.
EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine, ten.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: