Well. Base on my current experiences using Jolicloud OS (http://jolicloud.com), which features a fully operational linux based personalized distribution/operating system and web apps such as Google Chrome/Chromium-Browser web application, and full access to your virtual desktop via web browser, it is possible yes.
Have a look at this: Access your Dropbox from the JoliCloud Desktop
Basically, what Jolicloud does is to link your current Dropbox account into your JoliOS service/system, after which you can gain access to your file's list (and only the list itself) and choose which of these files you wish to download/preview, etc.
From the site:
Some media files like music, photos and videos can be accessed
directly inside Jolicloud. This feature depends on the HTML5 audio and
video codecs installed in your browser. If you are using Joli OS, make
sure to install the HTML5 Video add-on to preview media files.
Illustrations from the JoliOS Blog:
This way you won't spend your disk space in storing locally your Dropbox Files/Folders but you can choose when to use them. The next screenshot is from my desktop, which is JoliOS 1.2 Installed on a 8GB SD Card running in a HP Pavilion dm4 WITHOUT Hard Disk Drive, and where you can see that my Dropbox Capacity is 11.8GB (much more than my SD Card) and in the next screenshot you will see my current SD Card available storage which is yet 2.3 GB and running like a charm.
The same behavior is applied to Google Drive.
I can't say for sure how are the JoliOS achieving this features but this wide opens the possibilities for creating new services for the Dropbox Cloud Storage.
The richest feature on the JoliCloud Service is that you can gain access to your Joli's account from technically everywhere. Only Internet and an updated web browser is required.