tcasblue,
Yes, as part of the initial approval of the company, the FAA (or any National Airworthiness Authority) will have inspected and ensured the correct procedures are in place for stock control and processes to ensure their correct controls, They will not, however, do this for each and every aircraft or component.
Please remember that the company is audited several times before production starts and also after it has started. The authority also issues the ARC/CofA for completed aircraft until it is satisfied that the company can do it safely.
Quality Assurance = Making sure the processes are in place and spot checking for compliance i.e. Audits
Quality Control = Checking every product for compliance i.e. Independent Inspections