So it will be possible to run Linux applications on Chromebooks now, but that also means that you still will reveal yourself to Google in full, and they will know everything about you and sell your data to advertisers. You will not have any privacy at all because you still use Chrome OS with an active Google account that tracks everything you do. So no thank you.
Linux on Chromebook laptops is not a dual-boot operation. You're running both operating systems simultaneously. That means, for example, you can do things like clicking on a document file via the Chrome OS file manager and open it with LibreOffice -- without even starting a Linux session.