$1200?!
Be careful with the advice so far, I would just about bet the only other one that speaks from experience is kingharold, and he "wouldn’t stake his life" on there being any difference at all. $1200 in my book should be "Yes indeed obviously better now let me list the ways." Everyone else, would love to see them chime in again only this time letting us know what experience it is based on. (Would LOVE to see the guy admit his platter is 1mm off center!🤣🤣🤣)
I’ve run the same motor off AC, battery, and battery connected to and disconnected from charger. Heard distinctly the difference in each case- AC good, battery better, disconnected best of all. This was with a lead acid motorcycle battery on a Teres motor. Roughly equivalent, if not superior, to your CA. Solid experience in other words.
Battery power on my Teres brought a more relaxed nuanced and detailed sound to the music. Dynamics weren’t so much greater but were rendered with a lot more subtle shadings making them more lifelike. No one thing stands out as being different, yet the whole effect is to draw you more into the music. None of this speed stability BS. If people actually tried and heard it they would know. The errors people are talking about - 1mm - are just absurd. By the time you can hear it clearly enough to identify as a speed problem you are already beyond lost. Vintage 35 year old $350 Technics are better than this.
Since your CA is already designed to run on their optional 12VDC supply this means all you have to do is get a 12V lithium battery and charger and wire it up with a switch. Flip the switch to disconnect the charger when playing, flip it back again go charge when done. I was looking into these for my Soundsmith Strain gauge before deciding to go with Rens Heijnis and there are really good lithium battery rigs made for electric bicycles that are compact and already set up with wires and charging circuit. Couple hundred bucks and should be a piece of cake to adapt. Run your rig for days on a charge.