Yes. Sink water can pass through the disposer and its connections while the motor remains off, so a leak does not require a grinding session. Other connected discharges may also use that route.
What the observation tells you
Consider what was happening immediately before the dampness appeared: washing up, ordinary tap use or a connected machine emptying. Do not run another cycle just to reproduce it. Keep the area clear without touching wet electrical fittings or disturbing the mounting.
A useful next step
Report the appliance's off state alongside the water activity. That helps the assessment focus on the relevant water path without prematurely declaring the motor or housing responsible.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.