Chrome will only store a few items locally, and often you still need a network connection.

If you use Syncdocs [1], it syncs all docs locally as Word or Open Office files. It also syncs other files and Google calendars.

[1] http://syncdocs.com

I use insync[1], it also converts all documents, but why I use it mostly is it's linux support.

An advantage to Syncdocs is it's one time payment, instead of a subscription fee.

[1]https://www.insynchq.com/