Mister. Your ethnic group and ancestry is taken from your paternal side. Let me introduce you to what paternal side is. This is your father's, father's, father's, father's etc. lineage straight down that line. There is no pure race so thanks for stating the obvious.
He alongside with probably a few millions of Iranians claim to be Sadah families. A sayyid is a descendent of Ali ibn Abi Talib (ra) in the PATERNAL STRAIGHT line. And we know what ethnic group he belonged to and his ancestors.
So here you have their paternal lineage that decide their ethnic group in a traditional sense.
If their claims are correct as they openly proudly claim and display through wearing those black turbans showing that they belong to the Banu Hashim Clan, are not fully Arab is evident for all since there has been intermarriages. But it all depends when they migrated to Iran and who they married when they migrated to Iran. Obviously people of that stature, in the Islamic world Hashemites has been respected, would probably in most cases not marry your regular commoner.
Most of the Sadah families that went to Iran came after the brutal Safavid conversion of Iran from Sunni to Shia Islam. The Safavids to gain legitimacy (they themselves claimed to be Hashemites) imported Arab Shia Sadah families from current day Southern Iraq, Lebanon, Bahrain and the Eastern Province of modern day KSA. 400-500 years ago or so. They have been a social class by themselves within Iran even long before 1979. I am sure you know this and if not then I am sure that you can find local Persian books written in the nice Perso-Arabic scripture that tell you this. If not you can find Arabic books and English books dealing with this issue.
Read more here below: There are plenty of references. Look them up.
Safavid conversion of Iran to Shia Islam - Wikipedia, the free encyclopedia
There is a whole chapter called "Arab Shia Ulama". Let me quote it for you.
You are welcome.