It won't affect the gain, but it will increase the maximum available power - if you have enough drive voltage.
The 3S4 is rated maximum 67.5v on the screen grid, which is tied to the plate in the Quickie. It's reasonable to use a maximum of 72v (eight 9-v batteries) but not more. Note that the current will more than double, cutting battery life to less than half. It also makes the voltage a bit more risky - for example, you'd probably want to put the top four batteries below the plate with only the lower-voltage ones on top.