They will eventually recrawl it and update an index but your ranking will be in the toilet by then.
Is there evidence that this is indeed the case? I've seen much FUD but no actual data that shows that a properly updated site (301 redirects, HSTS, robots.txt) is penalized.
It's FUD. Google has already confirmed that switching to HTTPS will not hurt your site.
>Do I lose "link juice" from the redirects?
>No, for 301 or 302 redirects from HTTP to HTTPS no PageRank is lost.