Saudi Arabia has shown that it is possible to accommodate three million people for the Haj. See link below. But it is unwilling to provide any sanctuary for refugees from Syria. Syrians must apply for a visa or work permit to enter Saudi Arabia. Under this visa/permit system many Syrians have entered Saudi Arabia, but it is overwhelming for the benefit of obtaining cheap labour. None of the Gulf States have a domestic policy on refugees and none are signatories to the UN Convention on the Status of Refugees.
The experience of almost all refugees is that if they have to flee, they prefer to stay in a neighbouring country. They do this in the hope that when the political or military situation improves they can return home.