Is this design idea viable?

Yes, in this particularly case one of them would be shorted by the common ground if connected.
The SMPS model he indicated seams to have a separate ground from -V and from neutral too.
But sure, everything must be checked when playing with power components.

The best option is to go for a linear 60Hz power supply.

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Another option is a single power supply feeding a bridge power amplifier - in this case you don't need the capacitor.
TDA2005 and many others can be configured as 2 channel stereo or mono bridge (2 channels feeding a single speaker).
Most class D works in this topology.

I mentioned dual power supply for class AB, since this is the standard for high quality and more high power amplifier.
So it's good that someone new to electronics knows about it.
 
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