By the time your filtered water reaches your return chamber it should be nice and clean ready for return to your tank.
Having further biological media in your return chamber would, in time, once the media is mature, periodically release old dead bacteria and bits of crud, which is how this media works, but it would then be returned to your tank!
In time I suspect you'd have issues with "bitty" water in your display tank.
I'm also not sure I'd be entirely happy about something being in the pump section which could hinder its performance. The pump section is for pumps only, and maybe heaters imo.