The schools my kids have attended have always welcomed a lot of parental help & input and parents do a lot more than just bring treats to a class party. The PTA has made some big changes and does a lot more than just bring treats. In my district we have School Site Council which is a committee of teachers, parents and in the older grades students who made actual decisions about future direction & budget of curriculum for a school.
What I have personally done is to volunteer in the classroom (until jr high) and find ways to help at the school after that. One year I tutored 8th graders struggling in Algebra. The closes I got to avocation, was to run for School Site Council one year. I've joined the PTA and while I've never been overtly active in the running of it, I've helped in various projects other than fundraising. And I've supported a friend who was on the local school board for 6+ years.
All this volunteering time really made it much easier when it was time to advocate for my kids needs. I knew the teachers, principal and other parents and in the early elementary grades what was really going on in the classroom.
I recommend volunteering at the school and with the PTA. The amount of involvement possible really varies from school to school. Getting to know the other parents at the school and the teachers is a huge help. This way you won't be one of the outsiders.
