The coup happened without him, so it still happens in TTL.
The only potential difference is what a different Baath Party strongman would have done. With the Baathists being fiercely secular and a Shi'ite theocracy next door, the Iran-Iraq War is still likely to happen.
Possible changes? Maybe a different dictator would have avoided using WMD, would have sought to appease the Kurds, or would have settled the Kuwait dispute peacefully. Someone else might also have been less effective at maintaining power.
Saddam said in his interrogations that the generals in the area made the decision to use gas. He might be lying, but also: Iran-Iraq War happens you're going to have Kurds helping Iran, which means backlash in Iraq. Might not mean WMD use, but the scenario around it might sweep the regime into using them.
Whether or not Iraq will 'like' the US or not depends on how we handle the Iraq-Iran War and whether Iran-Contra happens or not.
Kuwait might happen, might not. Saddam thought he could get away with it because we didn't make a clear statement on defending Kuwait beforehand, so depends on the scenario around it. If Iraq invades Kuwait, the US will station troops in Saudi Arabia, which will lead to an Islamic Extremism backlash. Or *bin Laden will have some other reason to hate the US.
The Invasion might be butterflied, might not be. If the Soviet Union collapses, the US will still be world-hegemon which means we might be cocky enough to try something like this. Butterflies in Iraq will probably not change the Soviet invasion of Afghanistan, which means that a proxy war will start there, which means Islamic Extremism. However, Afghanistan
might not collapse--a big reason for Afghanistan collapsing in the 90s was because of regional politics, which could change with a different regime in Iraq, but might not considering Iran, Pakistan, and Saudi Arabia won't change a whole lot. If Afghanistan collapses and Islamic Extremism is on the rise, *9/11 could happen even without the Gulf War. If 9/11 happens, the US, as world-hegemon,
will lash out, which means Afghanistan might be a target. If the invasion is handled well, it will embolden the President to do something similar. Iraq might not be the target though, especially with the Ba'athists being strictly secular. Dubya did have a huge role in the decision to target Iraq, and if he's gone the Invasion might be gone too.
So no Saddam might not change a whole lot--the butterflies might change Bush Sr. and Bush Jr., which will probably mean no invasion.