Disclaimer ---I am not an expert, but this is stuff I have gathered through research! ---
In my opinion, I think it could work but it would require ALOT more work on the reefers end. The sump, skimmer, refuge, and any other media used in the reef tank are just ways of removing nutrients from our system. The high water flow would help keep the excess nutrients in the water column, but keep in mind too much flow could affect what you can and can't have (ie, fleshy corals needing less flow, LPS
needing more flow).
So basically, without all the mechanical and chemical stuff people use, the reefer would need to do alot more siphoning and be alot more thorough while doing the clean up.
The sump makes life alot easier and really just gives options to reduce the maintainance required by us to keep up with removing those nutrients. Also the sump helps clean up the display so that you don't have the heater, skimmer, cords, etc in your face that take away from the beauty of our small pieces of ocean.
If you keep up with the siphoning, water changes, and watch how much you feed, then no you dont NEED a sump, but I don't think I would want to try to reef without one haha.