You would think it would work, but if you are putting soil roots in water, it may not be that happy. Plant the seeds in oasis cubes. Let the plants grow in a tray with hydro solution until the roots are established. Only the bottom of the cubes should be wet. Then you can put the plants in the net pots with just the bottom touching the water.
Water roots are different from soil roots. The roots in the water need to be water roots. The roots above the water are air roots.
Try water cress they are easy to root in water and would be an easier subject than pansies. I have had mixed results with using plants grown initially in soil for hydro. It does work in hydroton, coir or cinder beds to plant the seedlings grown in peat lite. We grew the seeds in a plug tray and transplanted them out to the cinder beds when they were about 2-3 weeks old. We have an ebb and flow system so the roots are not submerged all of the time. The beds that clogged and were swamps, grew very stunted and sickly plants. The only things that tolerated the swampy conditions were plants adapted to growing in water or at the water's edge like watercress and water spinach (it would be illegal in some states to get certain kinds of seeds like ung choy. Carrots cannot be planted in rocky soil, so we lined the bed with a fine mesh screen and used coir and perlite. The hydro solution was sprayed from the top on the bed and the drain was left open several times a day to keep the medium moist. The carrots were harvested as baby carrots. We used the variety called Nelson.
As far as nutrient solutions go, you may have to find out the requirements of the plants you want to grow since nutrient solution often have to be customized for the crop.