As a system administrator in a high school with about 1,000 students, I can say in short: No way and this post totally misses the mark.
First and foremost, anything that is going to distract a student in class and is not educationally related will be blocked in school. Simple as that. Teachers have enough to manage in class or outside of class during normal school hours without having to deal with social media intruding into their work.
In regard to sexting and using Snapchat over traditional communication, I have not seen an observable difference in the frequency of issues pre and post Snapchat sexting. There are plenty of ways to save Snapchats that students know know to do, including such low-tech ways as taking photos of the phone displaying the message. OP doesn't consider that these images are sometimes sent to many individuals initially by the person who took the images. By that point, one of the students would most likely alert a school administrator. I'd say a larger indicator of when this would be a school issue is how many individuals it was sent to initially.