It’s not possible to just add data row to “any schedule”. Schedules in Revit are just tabular representations of the RevitDB aka your Revit model. What that means that they display what actually exists in the model. Following your logic of adding a “data row” to let’s say, furniture schedule would require to add a piece of furniture to host that data.
As a hack/workaround for things that we want to display in Revit as a schedule people have been hacking KeySchedules. Those are still representations of actual data in the DB and adding a new row to a key schedule results in a new set of data being stored on a Category element. However, they don’t require that you create a physical model element (furniture, column etc.), so you can use a seldom used Category like Analytical Beams (my fave) and just add a lot of parameters to it, so you can run a Key Schedule on it. Does that make sense?
Here’s a link to how to make a Key Schedule: http://archi-lab.net/building-data-harnessing-grasshopper-to-schedule-data-in-revit/