Did Zeniba's hair tie help Chihiro in any way?
There is a scene towards the end where Haku warns Chihiro to never look back until she reaches the outer end of the tunnel. When she's about to enter the tunnel, she stopped for a while and started turning her head around but stopped at the very last moment. At the same time the hair tie sparkled. Its a very subtle scene.

Now Haku did not tell her the reason why. But if you are familiar with Asian cultures, looking back would have trapped Chihiro in the spirit world forever.
Yes, the hair tie did save her. At least in my interpretation.