I just tried this with a doc file, and the buzz was nearly instantaneous, within seconds -- 3 buzzes total.
Certainly it's automated.
Paranoid part of me says it's NSA keyword scanning. I feel a little insane suggesting that, but it's certainly conceivable these days.
The other possibility is Dropbox is indexing the files for search?
Anyway, using Dropbox unecrypted is a terrible idea. EncFS has user-friendly frontends like Boxcryptor.