The right wing nutjobs have already gotten their way. Instead of discussing the embarrassing performance of the national team people are debating where Özils allegiances are.
The media can be split up in two "good cop bad cop" camps on this topic, one which is frothing at the mouth and which is close to asking for Özil to be deported, and another of the faux-liberal WashPost kind who while acknowledging the pathetically transparent attempts by the DFB to deflect from their failures still slam Özil for being irresponsible and in many cases finish their op-ed pieces with condescending garbage a la he should've stayed home both for team performance and "his own good".
The overall political discourse has shifted to the right even further, I even had discussions in recent weeks over why Özil doesn't sing the national anthem with people I talk to on voluntary terms which I never thought I'd have to.
So yeah, resigning or not makes absolutely no difference to the fact that the right has long won already. It's just a decision on whether he wants to deal with this farce again or not.