I'm using an HP chromebook right now at camp because my regular laptop died. My experience so far has been pretty frustrating.
As you probably know, it can't run MS word proper, and by extension verbatim. That's a disadvantage right off the bat. Cutting cards and writing blocks just got harder. But let's get to the non-obvious.
Firstly, it's much more slow and sluggish than my regular laptop (probably due to less memory). This is problematic given that this is essentially Google Chrome in device form, which is a browser that is very memory-intensive. This is even more problematic during practice rounds.
Secondly, multitasking isn't the greatest - you can do alright with Pandora in the background and one, maybe two google docs open, but the usual 5 or more tabs I have open at a time on my regular laptop will not do so well on a Chromebook.
Thirdly, you're limited - as I said, it's literally just a separate device to access Google Chrome on. Although there are a lot of apps that can make up for the limited standalone functionality, they will oftentimes take up valuable memory on the browser proper.
Fourthly, Google Drive/Docs isn't great for debate. At all. Even with offline functionality, it's just not as streamlined as MS Word, or just having a regular laptop with files stored to its storage memory. Dropbox will also be a pain to use since you have to use the website, and the files also open within the website. Office Live, while a convenient app, isn't close to a full replacement for Word. I find that navigating between different windows is much easier than navigating between tabs. Generally, the whole Chrome thing means the chromebook is very dependent on the internet anyway.
Would I use this computer as a main debate computer? No, I'd take a regular laptop any day. It's faster and more convenient. As a side device? Solid maybe. For <$300 it's not terrible, but it's not something I'd recommend wholeheartedly either.