Yes, I've seen it a lot.
I went to a state infants school, and one of the teachers was the mum of one of my best friends. My friend got preferential treatment, and did the 'I'll tell my mum about you' thing all the time.
My two DDs went to a state primary and it was awful there. In elder DD's class, one of the girls was the DD of one of the governors. She always had the main part in plays, always picked to sing, always picked to read in church, always picked if there was a picture in the paper, and always represented the school whatever it was. It was the same for her two older siblings. She was good, but so were many of the other kids. I wasn't jealous, my DD was shy and wouldn't have wanted main parts, but all the parents got fed up of always seeing the same face. The girl was a bully too, and got away with terrible nastiness.
In the same school, the children of staff were always picked for everything. We had some amazing and very professional TAs, but there was one who was the mum of one of younger DD's classmates. She didn't work in their class, but was often on playground duty. Her DD was very bossy and liked to get her own way. The other girls didn't appreciate this, and refused to be told what to do, quite rightly. This girl would run to her mother and she would tell them all off for being nasty to her DD! They weren't being nasty, they were telling her that they wanted to share who made the decisions, not be told what to do all the time! I ran an evening activity (not to do with the school) and this girl came to it. She was very difficult and expected to get her own way all the time, so her mum was doing her no favours at all.