No. Grinding food does not separate grease from wastewater or make fat safe for pipework. Any separate grease-management equipment also has its own purpose and care requirements.
What the observation tells you
A disposer and a grease trap are not interchangeable appliances. Do not assume that one cleans the other or that processing smaller particles removes the need for a suitable waste-management routine. A clear-looking discharge can still carry material that causes trouble farther along.
A useful next step
Keep fats and oils out using an appropriate collection route. If the premises has additional waste-treatment equipment, ask its responsible specialist how the existing arrangement should be operated and maintained.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.