Battery Power Supply Yes_ or No_

It seems to me that a phono stage is at a greater risk to noise than any other gismo in a system.  Mine makes a slight hum, and I am considering saying "la byby" to it.  Some years ago Sutherland sold a phono stage that was battery powered.  The theory being that this arrangement would substantially lower the noise floor.  I am considering a Project phono stage that uses a 18 volt wall wort for a power supply.  It is a metaphysical certainty that some noise will creep up that power cable.  So my concept is to wire 3 small industrial 6 volt batteries together, such that they produce 18 volts, and chuck the wall wort..  I think most people who post here are further down the knowledge trail than I am.  I hope some of you will share your wisdom regarding the above.  Gratzi, in advance for your thoughts.
Power is just one of many ways noise has of getting in there. A battery is one way of lowering noise. My motor was at one point upgraded with battery power. It does make a difference. Even with the battery though it still needs to be disconnected from power or noise still comes in. Even then the power supply is but one small part of many. Everything matters. Focus on the battery if you must, but you'll be way ahead of the game if you put a lot more focus on the sound that comes out than the parts along the way. Only once you select the best phono stage that way, then you can look at tweaking different aspects of it. 

In other words buy the Project if you like it the way it is, but not because you think you're gonna make it so much better by replacing a wall wart with a battery. You will make it better all right. But not much. Not much at all.
I can share my experience with battery powering gear. With my CD player, a battery certainly lowered the noise floor but at the cost of decreased dynamics. This is most likely attributed to the battery being too small, not enough capacitance. A linear power supply works better here, at least until I get a larger, better battery. With my tube preamp buffer, it sounds much better on the same battery that wasn’t “good enough” for my CD player. It sounds better on that battery than the same linear power supply that makes my CD player sound best. Trying to relate this to your situation, the tube buffer is closer in function to the phono preamp than the phono preamp is to the CD player. The phono preamp isn’t the source, it’s a type of signal amplification just like my tube buffer (which by the way applies 9 dB of gain). I say give it a shot, if you know what you’re doing so you don’t accidentally fry a component, and see how it sounds. From experience and from what others have said, bigger batteries sound better in terms of dynamics. We’re talking 70 Ah or more. Yes, that’s like a car battery in size. Your mileage may vary and you may not need that much. I’m using 35 Ah for my tube preamp and it sounds great. The CD player obviously needs more. 
noromance.... what is the benefit of strapping a big cap do.  Please advise the logic or benefit of doing this?  
Hey, it’s Zipost! I need to give him a shout-out. Zipost was absolutely instrumental with integrating batteries into my system. Very knowledgeable. He even hand-built me some parts that I needed. My system has never sounded better! Thank you, thank you, thank you!
@zipost It was more of a rhetorical question seeking an answer than an answer itself. But wouldn't a capacitor increase the speed and recovery of the power supply?
@alwynlarryv.... your ideas are great, excellent approach and well thought! But it needs to be implemented and executed correctly.

Yes.....for sure will be a Big improvement if you can implement both the regulator & battery correctly. I recommend using only 24v lead acid battery for your application. The results are amazing; the sound can be described as extremely organic ( better imaging, bigger sound stage and overall better tonality).

No....The cost will be dramatic ( charger, regulator & battery) expect to cost more than the actual phono stage. I don’t recommend lithium, nickel cad, LiPo ( they all sounds really bad) that is due to BMS ( battery management systems built in the battery).   Your threshold is at 18v, you Shouldn’t series the battery, use a single 24v for Ultimate results ( pure and simple).   With phono stage application ( low signal & sensitive to noise) extreme implementation and execution will give you an awesome experience and one amazing sound quality.   Let me know if you have any questions, ideas, or suggestions.  Happy Listening!