choice field has it choices defined in field definition. I.e. if you will inherit base CT - by default your new CT will have the same choices. However also each CT contains own copy of each field in Fields property: How to: Reference a Column in a Content Type
The SPContentType object also has a Fields property that returns an SPFieldCollection object. You cannot add columns directly to this collection. When you add an SPFieldLink object to the FieldLinks collection, a corresponding SPField object is added automatically to the Fields collection. Each SPField object in this collection represents a "merged view" of the base column definition and any overwritten properties that are specified in the column reference.
So what you may try is to find reference on this choice field in inherited CT in it's Fields property and add more choices there programmatically. It should not affect base CT.