The multiversal labyrinth and its possibilities of a world do not know what I am not going to say and I will show them directly:
In the Otoko no Jouken drama CD, Simon grows up to become a notable mangaka who creates a story loosely based off the events in the earlier drama CDs and calls it Tengen Toppa Gurren Lagann. However, the Simon from this story, Simon Avant, walks out of the pages and captures the mangaka in his own core drill.
I don't know if that is manipulation of the plot, leaving reality or separation from reality, simply something illusory about the labyrinth (which would not make sense because there is nothing illusory in the labyrinth, the only thing there are are possibilities that are real and you can touch and feel and well what happens there will happen in reality) technically you interpret it as you want.
"Next. "When did Rosiu discover LordGenome?"Nakashima: Oh, that is written in a novel. I explained it in the DVD audio commentary, but that is a lie (laughs). Novels are sold by mail, so those who like logic is there, and those who like interesting are the DVD version. "Gurren Lagann" is a story of the multiverse, so the "Gurren Lagann" audience you believe in!"
in the novel and the dvd the reasons why rossiu got the head of lordgenome are different, but they are just as valid, because gurren lagann is not only the story of the anime, it is the story of the multiverse.
With this logic, any Gurren Lagann merchandise, whether spin off or commercial (dimagos, parallel works or video games) would be canon because they are part of the history of the Gurren Lagann multiverse.
and the otoko no jouken is something that comes from gurren lagann, it is a product of gurren lagann that is a different story from gurren lagann but it would be canonical because it is part of the multiverse