Currently, using the append geoprocessing tool does NOT give an error when data from the source is not in the domain of the target field.
Having a tool that can insert data that differs from a domain without error by default causes confusion when users aren't extremely familiar with the target data schema. Adding an option to the append tool that allows the user to opt in to error exceptions when domains, field types, or other schema definitions are in conflict would be a great addition to combat this.
The hope is that we could hand a strictly defined geodatabase (as in, it contains domains, non nullable fields, etc) to a client to fill with their own data, and they will be unable to insert bad data. The append tool is one of the major tools to start this process, and it does not respect domains.