The top issue of this topic should be about the Iran-Iraq War.
It would depend on whether the unnamed leader is Shia or Sunni. A lot of the issues regarding Iraq's foreign relation before 1979 had to do with Iran and its relation with Iraq's Shia Muslims. Iran also supported the Kurds during both first and second Iraqi-Kurdish War. The two wars ended less than 10 years before the start of the Iran-Iraq War. The hostility between Iraq and Iran, of course, went centuries before that. I believed Iran's support of the Kurds grew out of the Arab-vs-Persian and Shia-vs-Sunni conflict.
The Iran-Iraq War is probably the key issue in this debate. Before the start of the Iran-Iraq War, there were evidence that Ayatollah was destabilising Iraq through the Kurds and the Shia majority. At least, Iraq was very concerned. If the leader of Iraq is a Shia Muslim, the Shia-Sunni aspect of the conflict would be taken out of the equation for a few years. In 1979/1980, Iraq would be less concerned of a Shia revolution in Iraq. Without the concern, the chance of a war would be unlikely for a few years(there are many, other seasons why the Iran-Iraq War happened).
If the leader of Iraq is Sunni, I am not sure what would happened. Saddam was one of the main reasons why Iraq invaded Iran, but not the only reason. As mentioned, the Iran_Iraq conflict went back long before Saddam. A moderate Iraq leader might not go into the war with Iran in 1980. Things might get out of hand. Please do not forget. The Iranian Revolution in 1979 was also about a feverish religious movement overthrowing a secular state. Iraq in 1979 was probably one of the few secular states in the Middle East. That fever could eventually spread to Iraq and disstablizing the country.
Meanwhile, Saddam did accuse the rest of the Gulf States of egging him into the war with Iraq and Tehran also did try to spread its Revolution through the Middle East. Again, please do not forget the Iranian Revolution was also about the overthrowing of a monarch and founding of a republic.
I think a moderate Iraqi leader would not invade Iran in 1980. In a certain way, Saddam did counter Iran. Without the war with Iraq, Tehran would become more aggressive toward spreading its revolutionary ideas throughout the Middle East(hint the Shia Muslims in Lebanon). The Middle East probably would engulfed into something else that Iraq needed to get involved.