Could Shin Gojira have an exclusive trailer for the next Evangelion film?

We all know that there is a lot of cross promotion between Godzilla and Evangelion since the director of Shin Gojira is the director of the Rebuild of Evangelion series. There have been posters, shirts, toys and tons of other promotional goodies featuring the King of the Monsters and one of the most famous animes in the past 20 years. Is there a possibility that this could lead to a trailer for the 4th/final movie of the Rebuild of Evangelion series to be shown in theaters alongside Shin Gojira? It would make sense. Fans have been waiting a good while now for a trailer for the next Eva movie. With all the cross promotion, doesn't it seem possible/likely that if they were to reveal it, they would do it with Shin Gojira?