I think that kids disturbing a teachers wedding is relative to the age; if they are young they dont belong at the wedding at all, and if they really want to come let them come for kabalas ponim only. However, if they are a little older, then I dont see anything wrong with them wishing the teacher mazel tov; I would probably even say they should out of hakaras hatov.
In addition, I think what shteltzoo said depends on the teacher. Most teachers in todays day and age do not really care on a personal level. However, there are more than enough teachers out there who do care on a personal level and would go out of their way day or night to help a student. I dont think you can make a blanket statement in either direction