Sounds about as likely as that EU army that was supposed to make the EU independent of NATO, and thus, the US. How's that working out? The EU constantly talks about challenging US power (Macron and Merkel in particular), but almost never do. I'm sure this will be more of the same.
Well for one because with the current leadership in the US there is for the first time in history enough incentive to actually push through.
The unfortunate (for them) truth about the EU is that outside of its economy, the EU is irrelevant on the international stage. People want access to their market, but Europe cannot project any force outside of their own borders. Outside of maybe Iran, there isn't a single country in the world that curbs their actions due to fears about what the EU will do. Even countries inside the EU act without fear of what the EU will do, just look at Poland.
I'd even venture to say most people in the world don't even know it exists. People know about Germany, France, and those countries individually, but people only know about the EU because of the news Brexit caused.
The United States has allies AND leadership in every region of the country - Europe doesn't. If all this commotion has to do with the Iran deal, the other major players in the region (Israel, Saudis, and UAE) all have close ties to the US and will be following American leadership and ignoring whatever Europe says. So I don't even see how Europe successfully protects Iran in this case.
So sure, Europe can talk all it wants about how they want to get rid of US leadership. But American leadership is felt all over the world, and major countries in almost every region will follow the US and not Europe.
Sometimes having a big ass army, economic and cultural hegemony, and a history of being in other people's affairs gives you some clout.