no unless you keep it at 5.1.1 and don't upgrade to 6.0.1. even if the person saved shsh blobs it can not be downgraded. I kept mine at 5.1.1 and my jailbreak that is the only way.
Keep in mind for the 4s you need shsh blobs then you can reinstall 5.1.1 using the blobs. However if you update to current firmware you will not be able to Downgrade back to 5.1.1 at this time.