If the numbers are small based on what you expect, I think you are most likely working with data that are in decimal degrees. Your life would be a lot simpler if your script simply called
Add Geometry Attributes—Data Management toolbox | ArcGIS Desktop
and returned the area units in what you want, accounting for the projection that your data need to be in. If you try to do this through an update or other cursor, you will have to account for the projection as well as the unit change.
If you just need the information to be temporary, you can always add
Delete Field—Data Management toolbox | ArcGIS Desktop
to your workflow to remove the previously added field.
In short, it will cut down on potential errors. (both tools exist in arcmap and ArcGIS pro)