I don't think that's something I would wonder about, provided you don't write things like, "Today was so busy I didn't have time to do anything," because then it would imply the diary entires shouldn't have been written.
Frankenstein by Shelley comes to mind as a novel written entirely in the form of letters, and the climax occurs while the author of the letters is in the middle of writing. He stops, then comes back and tells the ending moments after it occurs in his "real time."
Lolita by Nabokov is written in memoir form, not exactly diaries or letters, so it's completed after the story has already happened.
Flowers for Algernon by Daniel Keyes is another, written in scientific journal entries and dated (not always daily) so the reader knows when the events occur, but not necessarily always happening that one day. If you haven't read it, it's absolutely brilliant and can probably give you a really good idea about how to convey time.
And finally, there's one last novel that I immediately thought of. It's YA, and something I read so long ago I couldn't possibly remember the author. "Dear Mr. Henshaw," I think it is, written in (almost) entirely unsent letters.
Hope this helps!