We do know that apps outside of the core applications provided, like Youtube and Maps, do allow them to collect information on how those applications are being used and to enhance the usefulness of them. But also, these applications will fall under SB187 when it takes affect July 2016.
The information collected from Google outside of the core education applications is anonymized and used for the optimization of the tools. Not targeted at advertising to students.
Thus, it looks to me like we have some relatively good protection for student privacy when using Chromebooks and related software. As always, we need to keep vigilant, and keep in mind that when we allow a state agency to supervise our children for a large part of the day, there will always be inherent risks to privacy. But based on the information above, I'm not too worried about the classroom use of Chromebooks significantly increasing that risk.