The key to this for me is simply the temperature and 02 content of the water.
If the water temperature is at least temperate and the 02 level at near saturation then there should be no problem growing bananas in water.
If the temps and/or 02 level are low then rot is very likely to occur.
I use something similar to stimulate rooting in pups when i remove them and then find they have no roots. Its a primitive aquaponic set up. The pups are held in a gravel basket suspended over the pond and are constantly saturated with pond water so they take 02 from the air and nutrients from the water. Its never failed to work for me yet.
