Unlike most new musicals, “Six” has come with a pre-existing fan base, mostly cultivated through social media on both sides of the Atlantic. Audience members are told “pull out your phones” during the show and encouraged to film one of the big numbers; many of them have done so, resulting in countless YouTube and Instagram postings, all building the hype. Criss Henderson, the executive director of Chicago Shakespeare, said he never before seen an audience at his Navy Pier theater react quite like this one.