This is a very difficult question to answer in that proving a negative is nigh impossible.

For example, the US and the USSR debated quite a few things in the UN. Did this prevent the Cold War turning 'hot?' That's unanswerable, I think.

Consider the Cuban Missile Crisis. Much of the drama took place in the UN. Did the fact that some of the discussion took place in a public international forum keep things in check? Maybe? Probably?

Consider the various military campaigns of the UN. First, understand that while various countries fight under the auspices of the UN, the UN cannot demand that any nation provide soldiers to fight. This means that while the UN flag may be on the center staff, the military action is actually one of the nation(s) that provides the soldiers.

There are myriad geopolitical reasons why a country may want to intervene in another country, but don't feel that a unilateral action would be appropriate. Doing so under the UN flag grants a level of putative legitimacy that a unilateral move may not attain.

Consider also the make-up of the Security Council. Any of the permanent members can veto an action. Does that fact that Russia (previously the USSR) and the US, Cold War enemies, have had veto power over any UN military action mean that the actions the UN did take have greater legitimacy? Did the veto power ensure that neither NATO nor the Warsaw Pact could push an aggressive action thru the UN? Did this serve to keep the peace? Maybe? Probably?

It's a far-from-perfect analogy, but consider a person who has received a series of vaccinations. That person lives their whole life without contracting polio. Did the vaccination keep the person from contracting polio? It's certainly possible, maybe even very likely, but it's impossible to prove. There are obvious problems in this analogy, but I think it's a fair way to guide your thinking.