NO.
At home, we work to get to the bottom of the real reasons for problems at school and work to find solutions (which takes way too long but...)
But you don't get punished twice for the same offence.
I WILL punish for school issues if the school does not... for example, if I catch my kid being a bully, even if the teachers miss it, I will call it with the normal at-home result. But not double trouble for one problem.