Yes and No. As @whyzar has answered, you can change the Allow NULL values property on the SHAPE field.
However, this will not stop features being added without geometry!
To emphasise the point at the end of @whyzar's answer, ArcGIS does not use this property to force a user to populate the field. All this property does is not record
NULL in a field, so if the user doesn't enter anything it will record
empty value (numeric = 0, text = "") instead of a database NULL
There is no notification telling the user to enter something, or not allowing them to save if they haven't.
To demonstrate, I have created two feature classes - one with Allow Nulls = Yes, and the other with Allow Nulls = No.
Screenshot of Allow Nulls = No
I drew in two new lines, and then added two records into the attribute table without creating lines. I was able to do this, including save/stop edits, in both feature classes without any message or warning.