As a filter principle, it works great... But for growing edible plants indoors you might run into light deficiency issues. But for a large number of ornamental houseplants, a regular aquarium light in the higher end range can do pretty well.
Aquaponics is nothing but a fancy new word and it doesn't imply one particular technique. You can go many ways to achieve a similar goal.
As for example, i have a tank with a sump filter below it, and there is growing a plant in this on top of the filters bio-media. And this is what aquaponics actually is, plants growing emersed on a filters media regardless in which place this filter is situated. Without a plant, it's nothing more than a "Sump/Trickle filter" with a plant it is "Aquaponics".
There are several techniques to distribute water from an aquarium to an external (internal) planted filter box.
This is one i made 2018 and works a treat...
https://www.ukaps.org/forum/threads...its-finaly-happening.48576/page-2#post-526775
This is in the garden also from 2018 similar fashion but externally with an overflow syphon.
https://www.ukaps.org/forum/threads/mission-bathtub-2018.52227/page-2#post-520817
It definitively works as a technique...
I doubt it'll work growing edibles indoors hooked to an ornamental aquarium. maybe some herbs like Basil, Thyme and Rosemary or some types of lettuce as long as your lights are strong enough. That's a trial and error to find out where you can go with this.
But mind to harvest some plants, you need to disturb the (filter media) substrate.. This can create a mess, not only for you indoors but also for the ornamental fish in the indoor aquarium. This is something you would like to avoid as much as possible. Or find a way to safely work around this.
Personally I would leave it with ornamental house plants only.