Absolutely not permitted at my district. If it helps build your case, even Amazon doesn't believe they should be in classrooms. The blurb below is more than a few years old from where I found it, but for what it's worth, the following was posted directly from an Amazon employee in a CoSN community forum:
I thought this might be helpful to the group. Amazon only permits personal and non-commercial use of Alexa. Alexa is currently not intended for use in classrooms (particularly where students under 13 years of age are using the device). If you want me to put you in touch with the team exploring future and potential use cases I am happy to do that. We do have a process internally to gather that feedback from schools.
Thanks,
Chad A. Stevens, Ph.D.
Strategy Lead | K-12 Education
Amazon Web Services