Answer

It depends.  The CXD-Q and CX-Q series of amplifiers are intended to be part of the Q-SYS network architecture, and always fed audio from the Core over the QLAN network.  However, it IS indeed possible to set up these amps for "Standalone" mode whereby an amp will revert to its "local" analog inputs whenever the network or Core goes offline. 

An amp's Standalone mode can be set so input 1 feeds all of its outputs, or for one-to-one assignment (input 1 goes to output A, input 2 goes to output B, input 3 goes to output C, etc.).  In addition, the amp will keep its filter/crossover settings as defined by the model of QSC speakers assigned to the various outputs, or by any Custom Voicing blocks associated with the Generic Speaker blocks assigned to the various outputs.

Once a Core is connected with a standalone design as described, the amps will then be "programmed" based upon the intended signal flow. If Standalone mode is enabled in the properties of the amp(s), you can then remove the Core and the amps will continue to operate as expected.