Not at all. You're connecting my answer to your question with an entirely different question that you also happened to ask.

The question I answered was whether or not an inverter would work with any DC power source. Within the limits of the inverter, it will. It does not matter if the DC was generated by rectifying AC, a battery or a duck flapping its wings.

Just to be sure you're entirely sure what's what:

A rectifier will take AC and make it DC.
An inverter will take DC and make it AC.

So that thing I linked would give you, from a DC EmPower port, a regular socket in which to plug your regular power supply. It's highly inefficient to work this way of course (you'd be rectifying inverted DC, which in itself was rectified AC already) but so long as your device does not operate at the limits of the 75W an EmPower port will give you, it will work.

so: DC Power Supply (empower) -> Inverter -> device (probably with its own power supply).