No
I've shipped complete barreled actions, and complete rifles including the bolt thru USPS with no FFL. Just declare it as a Barreled Action or Mach parts if it's just the bolt. Never had to open the package to verify contents. Just be honest about what you are shipping. If it's for repairs no problem. If Fore Sale, then yes you will need a FFL to handle the sale out of state. If in doubt, check with your own Post Office.