I am working with ArcGIS and Python and trying to append table rows into a feature class.
You cannot use append and you cannot just make a table view of the feature class and then try to append it in.
You cannot (or are not supposed to). When I worked at GDB team, we spent time every once in awhile fixing bugs for processes that create Null geometries. The reason there is a "Find Empty geometries tool" is to fix this very thing (since some gp processes can potentially create empty processes).
As mentioned in some of the comments, there are some Complex FeatureClasses that have some internals that rely on some geometries columns being NULL, but these are handled through special codepaths - you should not attempt to create this situation within ArcGIS because you will start getting unexpected behavior.
Don't do it :)
To get around the same issue, I created geometries for objects that had them, and default geometries for ones that didn't, added a flag called IsCurrent and set it to 1 and 0, in each case. You can easily apply a filter to view or update either.