Gobbling up Syria through war is a non-possibility, and Saddam's coming to power ended the prospects of Ba'athist political union and turned Iraq and Syria into arch-enemies.
Kuwait though could be possible. Previous Iraqi governments had designs on Kuwait, claiming that Kuwait was always a historical part of Iraq and had only been separated due to British imperialism. When Kuwait became independent in the 60s Iraq had tried to take it but was deterred by the British. The West might not like Iraq annexing Kuwait but I think 1980 is too early for anything like the Gulf War to happen. The other Persian Gulf states might not like it either but they can't fight Iraq in a war. For Iraq the diplomatic and commercial drawbacks of worsened relations with the other Gulf States could still be more than compensated for by the oil revenue from Kuwait. If Iraq has the combined oil of Iraq and Kuwait and avoids the massive drain of money and men from the Iran war then Iraq should be in a pretty strong position.
The effects on Iran of avoiding the war would be significant as well. When the revolution happened there were quite a few different ideas of what kind of government Iran would have and it was far from certain that Khomeini would come to power and institute a theocracy. In 1980 there were still plenty of people not too thrilled with Khomeini's take over, but the war with Iraq caused Iranians to rally together and to the regime in defense of their country. If there is no war Khomeini's position would be weaker. Additionally, Iran's economy would be a lot better off without the massive casualties and expense of the war.