She does not die. She finds out who he is, helps him defeat the dragon and rise into Area E, and figures out their feelings for each other before they go home. To the point I've caught up at I don't think he told Roxy the particulars of his skill, but his new harem member/maid knows and helps him deal with Gluttony's backlash. I say harem member, but it's one-sided, he's only got eyes for Roxy. Every other woman who wants him is kinda shit outta luck at this point.