Of course, if you plan on doing work, all your work files might be on your own computer, but without any apps on the Chrome Book, there is little you can do with these files, no local Word, Excel, PowerPoint though there are on-line editors. You can also upload your to a cloud service like GoogleDocs and access them over wifi. For work email, your company needs to have webmail service if you want to access that. But basically, this is a surfing machine and with that said, it might be limiting. When I surf only without apps, I'm often looking at rich media content (movies, YouTube, streaming video) all of which will be painful on the comparatively slow in-flight WiFi. You probably need to stick to more text & photo based content like email, Facebook, news/sports/weather, chat, eBay, on-line games, etc. BTW, the Chrome Books are (Adobe) Flash-enabled, not like our friends in Cupertino sitting on their iPads.
Sounds like a great deal though it is short lived (July 1 - Sept 1). I hope to try the service on my return flight if can get one of the first 20. If so, you'll see an update below, in fact, I'll write the blog post on the plane, having all the tools I need, courtesy of Google and Virgin America.
UPDATE: 7/22/11. Early morning at SFO. There are still Chrome Books available, but as I thought about it, I have my own laptop, an excellent MacBook Pro. Let someone who doesn't have a computer enjoy the Chrome Book because there is a limited # per flight. But I did play with the demo units at the Chrome Book station. It's great if you have no laptop for the trip, but it is limited to web browsing. There is the impression of apps on the home screen, but these are shortcuts/aliases that point to a URL.