Car Insurance payments and other bills such as Electric bills, Water bill, heating bills, rent payments etc do not show up on your credit report for making on time payments.
So paying Insurance Premiums each month will not increase your credit score or build your credit.
However if you default on the Car Insurance Payments then they might report it to the credit bureau's as missed payments which can then hurt your credit.
However if you charge your car insurance payment monthly to A credit card and then pay that credit card off in full monthly then you can boost and build your credit rating.