I think Oskari was asking about the noise of a battery as a PS
... They do have, less than a mediocre mains unit and so they need less filtering. But they do have a highish output impedance too, several times that of a well done mains PSU, even if our V-DAC with its 0'3A is not a big trouble to drive.
A good charger can be cheap too, but it will provide years or a lifelong service not only for your audio things, but for your car/bike/whatever too. Find and use a 'smart' one, not just a wallmart with a PS inside: lead-acid (be it SLA or gel or car open or whatever) chemistry batteries need ideally a CC/CV charge. This means 'Constant Current' (usually 1/10th ot its capacity, so 1'2A for a 12Ah one) first, until a defined max Voltage (14'4 to 14'8), then switch to "Constant Voltage" (keeping this 14'4V and lowering gradually the current until is less than 1/100th of the capacity: then the battery is 100% charged).
To do this a 'smart' chip is needed, but a quick search showed this one in the US:
Universal Smart Charger(1.5A) for 12V Lead Acid Battery en venta en eBay.es (finaliza el 01-abr-09 07:58:43 H.Esp)
See, this other one is more expensive and it is just a PS without smart circuit inside (so avoid it)
12V 9ah 10ah 12ah SLA Sealed Lead Acid Battery Charger en venta en eBay.es (finaliza el 07-abr-09 00:13:39 H.Esp)
And for people here in EU I have CTEK units (swedish), IMO the best ones (I have two of them).
With such chargers any SLA not discharged below 50% of its capacity can provide many many years of service. And they (chargers) are great for your car/bike too, they are smart so you can let them wired 24h/7d.