They don't; the Fastmail app is just a web view. It's completely non-functional when there's no internet connection. Really glad to find this out now, and not when I'm in an airport or something somewhere with no internet connection and really need to look at an email related to my travel arrangements.
K-9 Mail doesn't include a calendar, but it does come in at around 20 MB or less (for the app itself, mail storage not included) and it definitively works offline.
