Is it okay to have a ground plane with a Class D Amplifier?
So would it be acceptable to design a Class D amplifier, connecting
the amplifier's ground using a star connection, while connecting the
DC-DC converter's ground using a ground plane?

Ground planes reduce common mode voltages between components by reducing the resistance and inductance of the conductors between components. In the diagram below, the higher \$Z_G\$ is the more voltage the loads \$R_{L1}\$ and \$R_{L2}\$ will see. Now if you suppose that \$R_{L1}\$ or \$R_{L2}\$ are transistors, and \$Z_G\$ is a trace that runs back to the power supply. The first problem is if the current changes through the transistors, it will change the 'ground' voltage for both.
Lets suppose the current is 100mA through a 1&quot; 10mil 0.5oz trace (which will have ~50mΩ of resistance. The voltage (V=IR) generated from the resistance of the trace would be 5mV!
Now lets suppose we use a ground plane instead which would have roughly 0.3mΩ of resistance in one inch, we would only have a 30uV voltage generate from the ground plane resistance with a 100mA current.
It gets more complicated than that with ground planes because the current spreads out in two dimensions (and currents should be controlled in two dimensions for very low level designs), but the advantage of a ground plane having less resistance can be seen. In almost all designs using a ground plane is better than running traces.
If I were designing a two plane design and I couldn't have a ground plane and only run traces, I would calculate the trace resistance and simulate the design with the 'parasitic' resistance of the traces to see how it behaved.

Source: (pg 129) Electromagnetic Compatibility Engineering. Author(s):. Henry W. Ott.