I'd want to check the output of the invertor on an oscillascope before going down that route: I wouldn't be surprised if the output of the invertor was nowhere near sinusoidal, possibly much worse than mains AC. You'd have to check it under load, as most AC regenerators measure great until you load them, at which point they measure terribly.
IMO if you have 12v / 24v from a battery the worst thing to do is to convert it back to AC, only to have the power supply in your equipment reconvert it to DC. If you're going to go down the battery route then you should bypass AC altogether (except for the battery charger, which runs when you're not listening). If you google "Red wine audio" that's one example of using 12v batteries.