In part to make a counter-point to the (good from a different angle) accepted answer, I would argue it is not only desirable, but in fact smart from the point of view of the OP. Emails might not be the ideal communication tool (e.g. legally), but finding out how a given teacher performs from their former students is a very good idea. I have personally strongly advised potential PhD candidates to speak to former students, and it has been very profitable IMHO, at the very least to me (in as much as it has convinced applicants to carry out a PhD under my supervision), but hopefully to them as well! Choosing a prospective PhD supervisor is the most important and (more often than not) random decision that a student takes, so any access to prior information is useful.
Indeed, you should get from a former student information which
might not be accessible elsewhere, such as "is their style supervision
appropriate for me?"
I am aware it is not exactly the context of the OPs' question, but believe it could still apply at the level of a M2 course?
So in short I would personally regard a request for such information as
positive, I would ask my former students if they are happy to speak to the applicant, and proceed accordingly.
PS: Since others have mentioned variability with countries, my experience is European.