It depends on how they win, and it depends on what kind of win.
For instance, suppose that Saddam Hussein succeeds in his 'lightning war' strategy - a fast brutal blow against a weak and disorganized Iran that brings about the collapse of the Ayatollahs Regime.
Iraq wins and imposes its territorial aspirations on Iran. I'd say this wouldn't be huge. There's no stomach these days for massive border redrawing.
But I do think that Saddam might try to hive off the Arab-ethnic Khoramshar (sic) region as a new 'liberated' state, and perhaps occupy or turn it into a client state. It would make a terrific buffer, and it's got a lot of Iran's oil capacity. So an independent Khoramshar would really hurt.
The Iranian Mullahs collapse, Iran devolves into bitter civil war, or a succession of weak backwards governments ideally. Which leaves a power vacuum in the Persian Gulf.
Which means that the US needs a new client: Saddam Hussein. Who is happy to make nice, given that he's allowed his liberties.
Meanwhile, a screwed up unstable Iran is going to be a major geopolitical problem for US policy makers, considering that its next door to both the USSR and the bulk of the West's oil. Oops!
If it happens that way, then financially Iraq is far better off. The expenses of the war are a fraction of what they were OTL. Iraq doesn't go into debt borrowing from Kuwait, etc. etc. That's even without possible reparations.
Saddam has a lot more money to indulge in kleptocracy, economic development, throwing his financial weight around with poor arabs. I figure that Saddam would opt in for megaprojects - pipelines, highways, universities, bridges, nuclear programs. Whatever is big. Dictators always think in terms of big building projects. Utility is about 50/50.
Relations with Kuwait will be different. The Kuwaiti's will probably not mess with slant drilling Iraq's oil fields, or will be more easily intimidated not to do it. There's not going to be the same financial issues in place as in Kuwait and Iraq arguing about debt. The Kuwaiti government may be much more cautious. This may save them from invasion. Maybe, maybe not.
Assuming wild success - Iraq emerges as the dominant power in the Persian Gulf and the Arab World, essentially trumping Egypt and Saudi Arabia. Lots of political cachet.
Likely radical Islamism would decline, as the technocrats and technocratic movement could show a genuine win. Islamism is, in part, a response to the consistent failure of any model of muslim government in the middle east.
On the other hand, Israel gets to tout Iraq is a genuine existential threat. Israel's been having a hard time lately with existential threat's. The effort to ramp up Malaysia for the role is not going well.
But as much as the US is pro-Israel, it needs Iraq in the region. So it's going to be like Archie going on dates with Betty and Veronica simultaneously - awkward.
How likely was it to happen. Well, I don't think a smarter Saddam or tougher Iraq is the answer. For this to take place, you need Iran to be markedly weaker, or to make some disastrous early decisions the blow the game for it.
Of course, if its just Iran screwing up, and Saddam is no smarter, then we likely have the usual situation where a stupid arrogant man get lucky and wins one - he assumes its skill, not luck, doubles down and keeps pushing until it all blows up in his face.
As to what that blowup would be? Gulf War with America? Revenge of Iran? Middle-East Jihad and Israeli Mushroom clouds over Baghdad? War with Saudi Arabia? Who knows.
A smart Saddam would have probably avoided the war with Iran entirely.