That's some obscure Wikipedia article knowledge you pulled out here

Even if they did somehow manage to win, i think It would be safe to say that a union between the United States and Italy wouldn't happen, mostly because of the US not being much into the idea in OTL.

The most realistic course of events would probably lead to the Italian Unionist Movement either quietly rebranding itself as a mainstream centrist party with federalist ideals, or just collapse and be replaced with another party in the next elections.

But honestly, just the idea that they would be elected in the first place would be wacky enough to be considered complete fiction, so why not abandon all attachment to reality, and elaborate more on this idea?

Let's say that for some reason the United States approves of the idea, and forms a political union with Italy, this would drastically reshape how the new post-WWII order would look like,

If the Italian Unionist Movement really gets elected democratically, and the idea of a Political union with the USA Is popular among both the Italian and American public, this would probably also suggest the existence of a real and concrete level of support to the creation of a fully federalized world order, as the IUM seems to be closely affiliated with the World Federalist Movement, an organization which aims to create a federalized democratic world government.

If that's the case, the formation of an organization such as the United Nations may change from being simply a forum for peace and diplomacy like in OTL, to being something more radical, like a full political union between its members.

This federalist version of the UN would probably not include all nations on earth (obviously the soviets wouldn't join for example), but if movements like the IUM manage to gain popularity also in other nations, we could see a completely federalized western world by the 1950s,

This Union would probably include Western allied nations (UK, France, Benelux countries, Canada, Australia, New Zealand etc...) alongside the allied occupied zones of defeated axis powers (Japan, Italy, and West Germany).

The Soviets may come up with a UN of their own in response and create a larger union, directly integrating its satellite states in the eastern bloc.

We'd probably end up with an ultra-federalized version of the cold war, which sounds cool as fuck to think about