Unfortunately, no. Chromebooks cannot support our application. If enough Chromebook users express an interest, we hope to be able to make a version that is compatible.
In the meantime, you can use our web interface to view and download files in your SpiderOak account into your Chromebook. You will still need to install SpiderOak on another desktop computer and upload your files from there, however. It would not allow you to upload from your Chromebook or keep files synchronized between your Chromebook and other devices.