Yes, I definitely do that. I also show them the headband obtained from No Name to help identify it. Failing the OO clerics I will take it to a HanSui temple. The relic should be returned to its rightful religion.
The orcish clerics are at first unimpressed and just thank you. Later, they come back to you and ask to talk to you privately. Because you are a cleric of the Oldest Orc, they will grant you the respect of not forcing you to tell the truth via divine force.