NOT unless that they actually did something against them..
I once created an email with a teachers name, fooled around with some people... no insults, no nothing... just chatting.... and someone told the supervisor... they went to talk to me... and they FORCED me to log on to my messenger account, threatening on suspension...so did i, i had not logged in to my account after i added myself on my teachers account so the window popped out, supervisor BROWSED MY LIST, couldn't find a thing... she assured me that there was a way to see who you have talked to and the chat logs (i was thinking YEAH RIGHT) to try and scare me so i would confess... i denied it all... she said she knew it was me but she couldn't prove it... and I got off... i don't they can punish you IN SCHOOL for something you did outside of it... for example as if i egged a house and instead of the police taking me over my school expelled me automatically... unfair...
edit: i was 11 when i did that