I also think you're better off buying a portable PA that runs on batteries. Fender Passport, or something like that.
The truth is that when you put AC Voltage into a amplifier it converts it to DC for use internally.
So, if you're putting DC (battery) into an inverter, you're converting the Voltage twice.
The decision is somewhat dependent upon how loud you want to be. The system the OP is talking about putting together will be a lot louder and (IMHO) sound a lot better than a Fender Passport.
Anchor Liberty makes some fairly large self-contained battery-powered speakers that I linked in the other thread. See Bigfoot and Beacon.
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Another idea would be to use a Class D car stereo amp and a battery powered mixer.
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KICKER | KX400.2 Amplifier;