Is it doable in theory? Sure, given enough time and money any company (or, for that matter, many ElReg denizens) can build their own cloud with access and query restrictions.
Should they try? Why not, it's only government money and to the extent that the money goes to EU companies and citizens it can be considered as a stimulus package.
Can the EU, accomplish it? Maybe. This is t big question; their track record is not the best.
But the name needs to be changed. I suggest EuroCloud.