Depends on how close you make it. If it is directly under one of the barrels, then almost all of the gas will go down that barrel, with very little reaching the others. Put it just off to the side (so it has to change direction to reach the barrel) and you'll get better results. The greater that separation is, the more balanced each barrel will be, but the more efficiency you will lose overall. Most Big Gun cannons arrange their accumulator sideways to save height. Again, you lose some efficiency because of the direction change, but then the cannon actually fits below deck. There are buna-ball valve cannons arranged similar to what you've drawn, but they are also difficult to fit in 1:144 scale ships because of their extra height.
I shortened some of the fittings, and the cannon's gotten down to 5" in height, so it should fit now. Thanks for the info Kotori, I'll keep it where it is now then until I test one and see how it works.
So I've finalized the magazine design: 6" in diameter with nine layers of 1/8" Acrylic, and one layer of lexan to keep the Ball Bearings from falling down into the accumulator. The lexan will be what holds the ball bearings in place until they're fired, and it'll allow me to make several different versions until it's correct. I'm also going to be using a bushing instead of a bearing, more of a personal choice than anything. I may send them out to be laser cut, depending on the price.