Do immunizations help prevent sepsis in children?

SOME do, yes: Some immunizations are aimed at infections that are responsible for some causes of sepsis. Most are vaccines against particularly aggresive bacterial infections such as pneumococcus, haemophilus or neisseria meningitidis. All of those bacteria cause many cases of severe and often deadly septic infections per year. The vaccines have helped significantly reduce those numbers.

Yes, and adults too: Vaccination decreases the spread of serious bacterial infections through the population. Since the main route of spread is through children in school/daycare, vaccinating these children reduces the risk of infection and sepsis in their parents and grandparents.