It all depends of the teacher and the class, really. Some teachers are really strict, and others let you do whatever so long as your work is done. Of course "whatever" must fall under what web content is appropriate for school.

I prefer not to go on at school though. In my computer class this year (graphic design) we do real work for real people, not just assignments, so time tends to be a bit tight. The only reason I've gone online at school this year is for research and to find a few images.

I have plenty of time to go on and have fun at home anyways, so I just go on from there anymore.