Now media filled grow beds do provide a huge amount of filtration and one could (proving the fry don't get sucked into the pump) skip the canister filters if you have enough media based filtration to support your fish load and you move enough of your tank water to keep the water quality up to your standards.
But you are right in thinking something may be missing if you were just to simply hook a heavily stocked fish tank to a NFT pipe with no filtration and call it aquaponics. (The times I've gotten questions from people who have tried this because some one told them that aquaponics was simply hydroponics crossed with fish, the people were struggling with problems of fish poo building up and going anaerobic in the NFT troughs.) And a similar issue can arise with a heavily stocked fish tank flowing unfiltered into a DWC raft bed.
The trick is there is definitely bio-filtration provided by all surfaces in a system, however, you have to make sure there is plenty of dissolved oxygen in the water to go around and that it doesn't become depleted at some point in the flow. Excess solids building up somewhere in the system can cause this.
Anyway, there are some very low stocking density systems out there that are simply fish tank flowing to raft tank with a little pumping and supplemental aeration and that is it but again those are very low density systems and really so far only tested with tilapia as far as I know.
Most systems using rafts or NFT pipes have some additional filtration. Some have combo systems with gravel beds feeding rafts or NFT pipes since the gravel beds provide great filtration. Other systems have swirl filters or clarifiers and then bio filters or mineralization tanks or net tanks before the water flows into the raft beds.
However, if you are planning to use the aquariums that are already in place, you could simply continue using the current filtration if you wished and just send the filtered water through your preference of plant growing method before letting it return to the fish.