Is it possible to mud flexible plywood for archway?

I’m doing an archway in an existing entryway for a client. the flexible 1/4th drywall we had left over from another project isnt nearly flexible enough for this application. I know that I could score the back to make the bend, but wonder why can’t I just mud straight to the 1/4th inch flexible plywood we are using as backing?

my idea is attaching the flex corner bead to the 1/2inch drywall on the face and to the bent plywood underneath, then mudding smooth.

would an all purpose mud with glue already added be better? or a fast drying joint compound like 20 min quickset? maybe even doing quickset with some added wood glue or drywall glue for extra adhesion? could also rough up the surface with some 80 grit.

thanks yall