First off, I was there in theater and I do not know what all has been declassified over the years (I do know some things have not been declassified yet) but have neither the time nor luxury of investigating that and will stick to Open Sources and opinion.
On 02Aug1990, our pagers went off and about 3 hours later my unit was feet wet over the Atlantic, completely unsure of what was going on. I was a wet-behind-the-ears noob, and only temporarily attached at the time. All we knew is that something happened, an embassy hit the big red panic button and needed help beyond what the USMC was able to offer. When we launched, the pilots did not know what country we would land in. Originally we assumed Israel, and then to our unpleasant surprise - Saudi. Forward a few months later, and some of my best friends and I were inside Iraq, waiting to see if there would be a massive series of hostage rescue strikes or not. Dammit, there wasn't, so we left.
As part of the coalition response, you had the entire array of the worlds antiterrorism community in theater. This included America (the unit - A and C squadrons, DevGru, 1/75th Ranger, elements of every SF group, elements of every SEAL team, even FBI Hostage Rescue), UK (22nd SAS, RMC, SBS), Canadian SAS, Australian SAS, French GIGN, German GSG9, Swedish SSG, Norweigan FSK, Polish GROM, probably several more than that, but 30 years later things start to get fuzzy. At the time, even Soviet liaisons (Spetsnaz and Spetsnaz Alfa) units as Iraq was holding Soviets hostage also, although their units were staged elsewhere - I heard Iran & Azerbaijan. Although the Soviet Union did not join the coalition, it was subject to increasing domestic pressure at it’s citizens being held hostage. The Soviet Union stopped trying to mediate, and stopped trying to put any kind of pressure against the UN resolutions and mandate and supported them fully. At the time, there was an estimated 5000 foreign hostages including 3000 Soviets, 900 Americans, and a mix of other nationalities. (3)
Your question seems to be binary and acting under the assumption that as long as Saddam held hostages, the international community would not intervene and invade the Kuwait/ Iraq theater with the intention of liberating Kuwait. The UN Security Council and international leadership was dedicated to several positions - the release of hostages, Iraq exiting Kuwait, and restoring Kuwait as an independent nation. As time passed, politically it became increasingly untenable to Iraq to maintain hostages and “save face” politically and with traditionally friendly nations that were allying with the Coalition. As Saddam was branding himself as the true Arab Hero / Arab Conqueror, the Coalition went and spoke very publicly that true Arab heroes do not hide behind the skirts of women or children. (1) . Subsequent UN resolutions made very clear, that Baghdad would be held directly liable for the hostages well-being, and that taking civilian hostages was in direct violation of the Geneva Convention. (2) Which could have also led the Coalition from not stopping at the border, but then going directly into Baghdad and then holding international war crimes tribunals… There was no “as long as they have hostages, we won’t invade.” The longer they held hostages, the angrier some countries became, and the farther the invasion would have happened. The Coalition ejected him from Kuwait, and smashed the army in retreat, and stopped. Your binary assumption is incorrect, and an invasion would have been green lit, but with potentially far more dire consequences for Saddam and Iraq once the UN decided to hold them directly responsible.
Politically, Saddam was hoping to find a public relations/ mediated way out of this. From the WaPo (3) article:
Saddam cited appeals by other Arab leaders, expressions of concern about war by U.S. Senate Democrats and pleas from a European Parliament delegation as positive factors in his decision. He said all this "encouraged" him "to respond to these good, positive changes -- changes that will have a major impact on world public opinion in general, and U.S. public opinion in particular, in restraining the evil ones who are seeking and pushing for war."
However, as the United States Secretary of State James A Baker told congress:“It does not lessen, nor should it lessen, our determination that Iraq's aggression against Kuwait must be reversed by full implementation of all the [U.N.] Security Council resolutions." (4) If he kept hostages, or let them go, the Coalition was dedicated to kicking him out of Kuwait.
Releasing the hostages, or keeping them was not going to deter the UN resolved Coaltion. Saddam was probably trying to avoid War Crimes/ Crimes Against Humanity charges, and politically do “something” to try and move towards getting the rest of the world into allowing him to keep Kuwait Mother of all Battles did not quite work out like he planned.
Some reading material:
https://adst.org/2015/07/freeing-american-hostages-in-the-first-gulf-war/ (1)
https://www.nytimes.com/1990/12/10/world/standoff-gulf-hostage-exodus-begins-iraq-75-come-hiding-kuwait.html https://irp.fas.org/cia/product/iraq_human_shields/index.html (2)
https://www.baltimoresun.com/news/bs-xpm-1990-12-09-1990343094-story.html (4)
https://www.theatlantic.com/national/archive/2011/02/the-mother-of-all-battles-20-years-later/71804/
https://www.foreignaffairs.com/articles/russia-fsu/1991-06-01/moscow-and-gulf-war
https://history.state.gov/milestones/1989-1992/gulf-war
https://www.chicagotribune.com/news/ct-xpm-1991-03-12-9101220963-story.html
Not a horrible recap, even though it is Wiki: https://en.wikipedia.org/wiki/Gulf_War
For fun: https://sofrep.com/news/ranger-history-the-persian-gulf-war/
Irrelevant to the question, but worth noting:
https://www.army.mil/article/161166/Operation_Desert_Storm_Remembered_By_Those_Who_Served/
https://gulflink.health.mil/timeline/fast_facts.htm
http://www.armyaircrews.com/blackhawk.html
Until Valhalla my friends.
https://apnews.com/article/0239d33021c62c008393a02fadfcc7ef
And especially in loving memory of Sergeant Major Patrick Robert Hurley, Master Sergeant Eloy Angel Rodriguez, and Master Sergeant Otto Frank Clark. KIA 21Feb1991 in a CSAR/Medevac mission. Angel, your kid turned out great. One of the best pilots the 160th had. Cheers buddy.
https://www.specialforcesroh.com/index.php?threads/hurley-patrick-robert-pat.27326/
https://www.specialforcesroh.com/index.php?threads/clark-otto-frank.27325/
https://www.specialforcesroh.com/index.php?threads/rodriguez-eloy-angel-jr.8644/