Is the following scenario legal
Let's say that there is a student A, who sends student B in a personal email but on school campus and on school wifi. Student A's email includes derogatory description of the principle. Let's say 10 days later, there was an unrelated riot inside of a class which the school administration for some reason believes that student A has caused the riot; student A is called up to the office and the office asks him/her questions regarding the incident.
Student A denies any knowledge but the school decides to go onto his/her school issued laptop and logs onto his/her gmail account and discovers the email and expels him/her.
Does the student in this case have the right to sue the school?
Because I believe that the freedom of speech in the USA should protect him correct? Especially because the cause of this whole incident would be unrelated and furthermore, there was an unreasonable search of his personal account?
My friends and I were talking about this scenario and have arrived to different conclusions and have argued about whether the student has the right to sue.