Jorgen,
I have not looked into this area for audio, but I built and used an off-grid micro-hydro power system from 1984 until 2007. I had a very small 24 volt turbine that charged a bank of lead-acid golf cart batteries, the battery wired to the inverter and a dump circuit (water heater) to keep the battery from over charging. Since the turbine produced 24 hours a day whether or not we used the power, we needed somewhere for the power to go. In your arrangement the charger would take care of regulating the battery charging.
So I know it is possible, but as mentioned, the question is how quiet it would be. There were many developments with inverters in my time, and they got more quiet with "sine-wave" inverters, but they were not pure sine wave and had noise in the output, and though regulated, voltage could move around a bit.
Also, a charger has its potential electronic noises. These would be important areas to look at carefully. Using batteries for audio noise reduction, you could easily defeat the purpose with the wrong charger or inverter. Since the charger wires to the battery and the inverter comes off it using the same terminals, any noise can go right across the battery.
Special batteries designed to deep cycle (car type batteries are designed for very high output for short periods and not to cycle deeply) would be needed. Deep cycle batteries have voltage and amp hour ratings. Other than getting the right battery for the job (acid, lithium, or whatever) you would need to calculate the optimal battery size for your instantaneous surge use and to sustain your general output, including the inverter inefficiency. And DC power with batteries can be dangerous!
It would seem to me also, likely better to do without the inverter if possible, like Raven suggests, but this is a whole different arena, to bypass the AC of your amp.
And there may be quiet inverters now. But I find that everything matters with our transparent gear, and for me, even a PS Audio P5 imposed a notable sound signature in my system beyond the benefits of voltage regulation and "clean" power. It all has to go through wires and circuits and caps and receptacles, etc, and each of these apparently can be heard. I had to work with this a fair bit with cables, feet, a fuse and the addition of a Shunyata Defender to get the P5 where I liked it. I am really picky after years of careful system tuning, but still, to me the stock P5 was not transparent, even with PSAudios best power cable. And these are built for audio by smart folks.
Also, Steve spent a fair bit of energy on the Mini Torii power supply and VRs and the rest. So one trick is to clean the power before it without messing up Steve's voicing.
Below is link for a battery power setup for 24V, not exactly what you need, but it is from a guy who has done serious research and development on transparent power with reduced noise. His name is Dave at Pi Audio. He knows a whole lot about these things, and may be able to help you get to an effective solution.
http://www.piaudiogroup.com/BatteryBUSS.html