Signing up just means making you easier to find. And if you refuse to sign up for the draft, there are some consequences, although to be honest, I don't know what they are. Over the years, I've been asked multiple times on job applications or in interviews whether I had registered for the draft.
I grew up in Germany, and crowds in the US blew me away when I moved over here...like...people would actually jostle you and bump into you. I could walk through a huge crowd in Germany and never feel like anyone touched me.