If there is a high impedance fault in the mixer, meaning a fault that permits _limited_ current to flow to the frame of the mixer, then with the EGC disconnected the frame will become energized. Someone touching the frame could feel a shock.
If this fault is not corrected, but the EGC is connected, then this current will flow through the EGC back to the neutral bond at the service panel, and from there back to the transformer. This will _reduce_ but not eliminate any touch potential on the frame of the mixer.
Someone touching the frame of the mixer would be placed in parallel with the EGC path, and _might_ still experience a shock. But a good EGC path will probably eliminate the shock; with a high impedance fault and a good EGC the touch potential will likely be reduced to the point that no shock is experienced.
With a _low impedance_ fault, a shock from the frame is quite likely while the circuit is energized, but because lots of current is flowing the breaker will likely trip quickly, eliminating the shock hazard. The shock hazard exists because of the voltage drop in the EGC with the high current flow.
In a mixer with no fault at all, if the EGC is not connected, there is a good chance that someone touching the frame will experience a minor shock due to the _expected_ leakage current. Capacitive coupling from the motor windings to the frame or minor and acceptable leakage across insulation can energize the frame. This current should be very low, in the microamp range. An EGC will remove this shock hazard.
In a system with moving parts you also have the possibility of electrostatic charging with no fault or leakage in the electrical system. I'd think this is unlikely with wet dough...but a possibility to consider especially if the mixer is used first on dry ingredients. An EGC will also act to drain this static charge.
-Jon