But you would get a "first" appointment instead, since the local system won't know about the USA vaccination. The second vaccination is identical to the first, so it amounts to the same thing. You just don't turn up for EU dose2 since that would be dose3. In the UK we would just enter the USA information manually first into our database, backdating it to the actual date and then enter the "first" dose as the second dose. There is a button in place to facilitate that, so I doubt elsewhere in Europe would struggle much with this. I know it works in the Irish Republic, for example.