4 wire Dryer with 120 volt motor on 3 wire circuit is it a liability to connect ?

[kwired]

This is more than just word games because, among other things, there are rules that allow you to reduce the size of the neutral relative to the phase wires, but you cannot generally do that to the EGC.
Before you go any further, you need to double check the gauge of the "ground" wire in the branch circuit.

More of a problem with ranges than with dryers at least in most cases. A 10 AWG multiconductor cable likely has no reduced sized conductors, as the EGC for a 30 amp circuit still needs to be same size as the ungrounded conductors.