Nice plant.
Once the adventitious plants form from the nodes on the inflorescence, they take up their nourishment from the water, not the parent plant. You can leave them, as suggested, until sufficient roots appear so they can be individually planted--and you will find there are two plants at every node, so you can separate them or leave them together as a "plant."
You can also cut the inflorescence off at the crown of the parent plant and leave it floating. I sometimes stick the cut end down behind a rock, to provide a stem of small plants which is handy in the corners of a tank. Sometimes I move the inflorescence to another tank. I find that the adventitious plants if left on the attached inflorescence tend to develop algae; I suspect this is partly due to the plantlets being closer to the light, but perhaps also because the light is of greater intensity than the plant's nutrient needs can balance.
You can also break off the adventitious plants and leave them floating. In the main tank, algae again frequently attacks them, which is less of an issue if they are planted to moved to a smaller tank.
Byron.