I recommend another good book by Michael Cohen: "Strategy and Politics in the Middle East 1954-1960. Defending the Northern Tier" (2005). This book is available online. The author continues with the same conclusions.
Yes, at the beginning of the Iran-Iraq War, the USSR even banned military supplies to Iraq. But this was done only for the sake of a good political position (instead of the USSR, Romania supplied ammunition to Saddam Hussein with Soviet consent). In return, the USSR obtained from Iran the right to fly its naval aircraft over Iranian territory to Indian ocean, and two or three Soviet radar stations operated in southern Iran for several years.