Bear in mind though that they are trying to spend their way out of a deflationary spiral. If they got it just right, things could balance out. Chances are a gazillion to one against it, unfortunately.
I see little chance that the Eurozone would be unaffected in the case of US inflation. Exporters to the US would find that their income from there would be worth less and less ... indeed a very weak dollar anytime soon would mean the end of my job, and a lot of others.