I voted yes...but with a disclaimer lol.
Given the fact that the EU occupies a landmass that's smaller than the US, it makes perfect sense for them to "team up" on certain shared services.
For instance, it doesn't make sense for them to have 27 different versions of the FAA. It makes sense for them to team up on some defense capabilities. 27 disjointed air forces are less effective than 2 or 3 bigger ones that are the result of collaboration with a few decision makers steering the ship.
And given the close proximity, certain border travel agreements make sense. (I wouldn't want to go through a lengthy customs process every time I went to Pennsylvania)
But I do think it should be more of a federalist model, where there are certain "infield" and certain "outfield" aspects.
Structured more like a federalist system like we have in the US, where the certain "key" initiatives are mandatory buy-ins (the infield), but where each member nation/state still maintains the right to "go their own way" on stuff that's not of international concern (the outfield)
The one potential flaw I see... Their HQ needs to be in London or Berlin, not Brussels.
The seat of any international organization needs to be in a place that embodies a more diverse set of viewpoints that would be more likely to be amicable to all parties involved. When you place the HQ in an ideological bubble (within the Overton window you're working with), that leads to contention. The UN HQ being in NYC would be an example of that.
