No. Compatibility must be confirmed for the exact disposer, pump and installation. A pump accepting ordinary sink wastewater does not automatically mean it is suitable for the discharge from a food-grinding appliance.
What the observation tells you
The two manufacturers' permitted inputs and installation requirements need to be considered together. Do not use a successful short run as evidence that the combined system can handle regular loads. A downstream pumping problem can also affect the sink even while the disposer motor operates normally.
A useful next step
Give the engineer both model references and the connection layout. Ask for system-specific advice before continuing to send processed food through an uncertain arrangement.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.