Is that your return pump on the left most chamber? and yes, I would prefer to keep my live rock in the display tank rather than the sump, but you can get away with having it in the sump as long as you clean it up once in a while. The order from left to right of my sump setup would be the water from display tank going down into a filter sock (I use a filter sock but I also clean it out every couple of days, some or even most would be successful without filter socks as well), next going to my refugium with macro algae (also optional, some might use this chamber for their skimmer or media reactors as the water level here stays the same), then lastly the final chamber for the return pump to send water back into the display.
But in your case, you could possibly run a gfo or carbon reactor in place of the bio media and sponge pad.