I agree that in the general case it's very unlikely for your average developer to be truly productive on day one, but I wouldn't say that nobody is. This is a large part of my value prop: I spend the first day or two getting infodumps to get up to speed, but even during that time I'm building up plans of attack to get done what I'm being paid to get done (and to me and to the people paying for me, that is productive).

I'm a consultant/contractor (depending on the gig), though, so the social dynamic is different and it's less about integrating into a team and more about understanding the exact problem domain.