The premise is unlikely. In the post-WW II world, one nation simply invading another nation and annexing all or part of it is a gross violation of The Rules.
The nearest anyone has come to that:
North Vietnam invading and conquering South Vietnam; except that the two states were recent divisions of a single country, and North Vietnam's attack was resisted by the US for many years with great force.
Goa, Western Sahara, and East Timor were all colonial enclaves seized by dominant neighbors; East Timor was given up, and Western Sahara remains contested.
But if Saddam got away with annexing Kuwait...
First, it scares hell out of the other Gulf states; none of them are strong enough to resist invasion. All would have to make explicit defensive alliances with major powers that would include at least "tripwire" ally forces based in their territories. Russia is allied with Saddam, and the US clearly couldn't be relied on. That leaves China, possibly France, possibly India or Pakistan.
Second, Iraq becomes much stronger. Iraq borrowed a lot from the Gulf States during the Iraq-Iran War. Its debts to Kuwait are eliminated; Iraq can also repudiate its debts to the other Gulf States. Iraq will try to claim Kuwait's sovereign wealth fund; if they get it, that eliminates Iraq's debts to outside countries.
Iraq will have an enormous cash flow. Possibly enough to disrupt th Gulf statesl,