Duracell 660 Powerstation to Run my System off of the mains?

your amp and each component needs DC. However, none are set up to take straight DC. They need 120v ac and then they rectify it.

Your power bank has batteris, but does not provide DC. It has a relatively cheap inverter that proides crappy AC.

Your powrbank has a charger. The charger has to be at a slightly higher voltage than the battery. The charger is a simple, and likely crappy DC voltage since batteries don’t need a high quality DC source.

So if you plug your amp into the powerbank, you’ll be running off the crappy charger, through a mediocre inverter, to your normal power supply to your amp.

"pure sine wave" inverter is what the PS Audio power plant uses.  So why not stick with something designed for audio use?  

Jerry

I would try grabbing the low hanging fruit which I mean powering the components that have external wall warts with smaller lithium ion battery power banks. Usually that means the dacand a streamer, Sometimes a preamp. This is a good way to make cheaper components so much better. Your larger components that are built for AC power do not lend themselves to this approach as has been explained above

What kind of inverters do litium ion power banks use?

If you can't answer this question why would you use them?

The issue is always how much electrical noise these units create. One way or another devices with "sine wave output" have noise and distortion on the outputs. They are essentially class D amplifiers which generate a 120V RMS output plus some amount of noise and distortion which most of us are unable to measure accurately. 

My personal solution is a Furman with voltage regulation (AVR) + SMP and LiFt.

It’s small, quiet, and keeps the output voltage to +- 5 Volts, shuts off during severe under / over voltage and is also very power efficient with lots of current capacity.

@Carlsbad2 I don’t know how a lot of things work but I use them if they improve my system. I’m not an elelectrician so I go with recommendations, trial and error.  I appreciate the information though as I do try to understand the basics! Cost is the main reason I don't buy a PS Audio Power plant. I have a Duracell 660 for my RV so I thought I'd ask.