I am planning on testing a PoE evaluation board (https://www.analog.com/media/en/dsp-documentation/evaluation-kit-manuals/dc2093af.pdf) with a pwm motor circuit. The PoE evaluation board doc recommends putting it Vout through a dc/dc converter + PWRGD signal before supplying power to whatever device/circuit you are using. What would happen if I didn't do this and connected the Vout and GND to the pwm motor circuit?
Your POE board DOES NOT require a DC-DC converter on the output.
The datasheet for the demo board you linked to clearly shows it configured with an active direct connected load.
The datasheet for the LT4275A shows a DC-DC converter, but this is for different reasons:
The input is via a bridge rectifier, so the ground is not contiguous with the source end.
To get the highest power down the data cable you need a high voltage (60V), so in most cases you need a DC-DC buck converter at a minimum to regulate the supply to the client needs. The switching converter transforms the power requirements requiring less current on the data cable.
PWROK ensures that you have the ability to gracefully turn ON/OFF the client load. You don't have to use it, but it's certainly best practice. However you could use PWROK to manage the client load side and NOT use a DC-DC converter.
Notice in the schematic above that the DC-DC is an ISOLATED converter so that the source and client grounds can be connected if required.
You have not explained what power or voltage level your motor requires, so it's hard to give advice. Most POE applications will use the maximum voltage possible to get the highest power transfer at lowest data cable currents.
So for example if your motor is a 12VDC brushed motor, drawing about 1A in your application then you consume about 12W.
If your POE voltage is 12V, then your data cable must carry 1A which will be problematic and non standard.
If your POE voltage is 56-60V then you only need to carry about 200mA, but require a DC-DC at the client end to produce the 12V required for your load.
NOTE: You also need to critically consider the client side capacitance (Cport in the schematic). You need to minimize pulse current drawn through the data cable. Many DC-DC convertors use a fixed current limit in the converter and you need to supply this pulse current from the local capacitor and not via the data cable. For example an LM2596 based switcher pulls 4A pulses from the supply no matter what the load requires.
The data cable is a mostly resistive problem. You want to minimize the current flow at all times. You can use this calculator to understand the voltage/current/resistance/length problem for your POE configuration.
You won't have regulated voltage, so the motor will be at the mercy of the source impedance of the line and rectifier. This means that you may have unpredictable results if you put an variable load on the motor, because the motor voltage will vary with the load. Probably best to put a DC to DC converter to regulate the voltage, or YMMV.