There are a few chrome extensions/apps that support local functionality - basic calculators and text editors, and Google docs will be introducing these features soon too. Other than that, without a web connection you're pretty much hosed with a Chromebook.
However if you're using a Chromebook then you'll be keeping everything of value on the web anyway - your documents might be in Google Docs or Office.live.com, your project plan might be managed at liquidplanner.com or pivotaltracker.com, your expenses claims are all on expensify.com, etc.
My company already does this, so these days when I'm on the road with my windows laptop it is almost completely useless for doing project work without a web connection. This means a chromebook is not such a big step for me.
If you currently work with local MS Office documents, then consider the cloud alternatives - they offer most of the same functionality (there are some limitations) but with really cool collaborative features - we often have 6 people editing the same document at once. The idea of each person having their own copy of something, and the consequent problems with merging changes and distributing the latest version is just a memory for me
