Chromebook offline activities

Solution 1:

One of the problems with the marketability of the Chromebook -- that it only functions when connected to the Internet -- is also a misunderstanding. Google's Chrome OS doesn't have any locally installed apps like a word processor or spreadsheet manager, so many believe that Chromebooks are dependent on and useless without Wi-Fi or cellular data connectivity. But when Chromebooks ship on June 15, they'll come packaged with offline versions of Gmail, Docs, and Google Calendar.

Sundar Pichai, vice president of Chrome's product management, announced at the Google I/O developer's conference that the company has been using offline versions of Gmail, Docs and Calendar for months, and that not only will Chromebooks sport this feature, those three core services will be available offline to everyone this summer. Source - PC World

In Short: Yes, it has an offline support for three apps: gmail, calendar, and docs.

Additionally, 3rd party apps will also be able to build in offline support. Example

I should also mention that it has a card reader, and a built in media player. Meaning, if you have movies, music, or pictures on your SD card you can watch them regardless if you have a network connection or not.