It could be possible, my main concern would be providing a dormant period. You could have it set up to divert your water into a different grow bed with another crop. You would need some sort of plants filtering your water at all times or your nitrate levels will reach toxicity (250ppm+) and start to hurt your fish. You could do partial water changes and water other plants with what you remove.
Nutrient deficiencies would be pretty likely. You would most likely have to supplement and foliar feed your plants.
Please post some updates if you give it a try, I'd love to see it work!