Hi David,
Its hard to say if it would work. Only way you will know is to try it.
My thoughts:
Some plants, like coleus, root well in water and seem to need quite a bit to be happy. I have never heard of rooting a Zinnia in water. Or growing a zinnia in a hydroponic system. Most plants have built in shut off valves when they have had enough water (cactus and succulents are the exception). So, presumably, the zinnia would know when it had enough water. The biggest problem with hydroponic growing is that the water has to be oxygenated or the plant roots will suffocate. That is usually accomplished by planting in a soilless medium (clay pellets or gravel) and having the water constantly moving through the root system.
You might try putting a few drops of Hydrogen Peroxide in the bucket to provide more oxygen. That works well with cuttings that are hard to root such as Hibiscus.
Daisy
