Not entirely. Have Hajj in mind here. It has been ongoing for 1400 years. Don't forget ancient trade ties between Arabia and South Asia. Those ties date back to the IVC. I kid you not, there are scholarly works about this, just make a simple Google search.
More recently (pre-1947 and pre-1932) trade between the two regions was also common.
KSA is basically a melting pot in terms of ancestry, in particular and mostly Hijaz. It is deluded now because this lot tended to mix with each other as well as the city dwellers but it is quite evident. Similarly with the Eastern province or what we call the Khaleej (Gulf).
Ironically both sides of the pond (The Arabian and Iranian) have had mutual migrations and settlements since time immortal yet the governments have been at odds. Another idiotic dispute in the Muslim world.