Does either Mach3 or Mach4 have the ability to monitor the output of servo or stepper shaft encoders in order to better assure axis positional accuracy and motion control?

If not, is it correct that the Mach DRO displays operate on the basis of Mach commands rather than rely on feedback directly from the machine being controlled?

No, and yes.

It depends.
There are controllers that work with Mach which will do that. The CSMIO/IP-A is one and I think Galil, DSPMC and probably Kflop with K analog also.
The one thing they all have in common is they control analogue (+/- 10v) command drives/amplifiers. There are Step/Dir controllers that update Machs DROs from encoder position, the Hicon being one but I am not sure if it actually closes the loop itself or just uses the encoders for position update.

The CSMIO/IP-A controls the analogue command to the servo drive to keep the axis on course, it knows the position by reading the encoder from the motor, it then updates Machs position DROs with that information. Even if the servo drives are disabled the DROs in Mach will always be updated even if you rotate the motors manually, assuming of course that the encoders are still powered.
Hood

I'm using a CNC Drive DG4S-16035 - DC Servo Drive which has differential inputs for my 2 phase quadrature encoder. The DG4S expects step and direction inputs from MACH and uses the encoder to close the loop between the motor to the servo drive.

However, there is no encoder information available beyond the servo drive units. 

It's interesting and slightly troubling to turn off the dc power to the servo motors, watch the mill completely stop, yet Mach continues running G Code and updating the DRO displays like all is good.

You need to have the fault signal from your drives in an E-Stop chain so that Mach knows a drive has faulted. It is also advisable to incorporate the fault signals into a hardware E-Stop chain as well.
Hood

Yes, the fault signal will become part of both a hardware stand alone E-stop and the logic-E-stop before the machine is put into operation. Currently it's in a test configuration while the mechanical issues are identified and corrected.