To clarify, I have a Clearaudio turntable with a 12v DC motor. Clearaudio indicates that their DC power supply is voltage stabilized, yet they sell a separate 12v battery power supply. This suggests the stock power supply has some limitations.
Every design has limitations, they just don't tell you about them. "Voltage stabilized" can mean all sorts of things. But there are guys with $50k UPS regenerators who still hear differences with time of day, running off AC vs regenerator, etc. None of this stuff is perfect. Not to the degree we can hear.
A battery is a chemical process. It has been a while you may not be old enough to remember but the old lead acid batteries would fizz out explosive gas when charging. Might even see the bubbles sometimes on some of them. Newer batteries work on different molecules but the idea is the same. None of them produces power as perfectly smooth and silent as we want.
Then the power has to go from where it's stored to where it's needed. At low voltage this gets real important real fast. What I'm getting at, there is no silver bullet. Just a whole bunch of things that can be done better or worse. Study enough of them, you might well be able to make a better battery supply than CA.
The good news is they already have a battery option for your motor. This means it will be real easy to convert to battery. Probably all you need to do is connect to where the option would connect. I would use lithium ion and make sure to use a charger that not only cuts off when playing records but that disconnects from AC as well. Without this feature RFI will ride right across the battery and this noise will detract from performance. Been there. Done that.
R. Daneel Olivaw