Dave is on target. There will likely be some cross-over effect , but my guess is that it wouldn't be enough effect to cause problems.
After all, the goal is to sound good - and that effect shouldn't get in the way.
Jazz basses with conventional wiring have an circuit in which running both volume controls at 100% causes some volume cancellation. But back up one volume pot or the other about 10% and the effect goes away. Not a problem as far as I'm concerned.
i have a P body with a P/J configuration in which I installed stacked-knobs with separate vol and tone controls. Each knob base is tone, tip is volume. This never has caused any audible problems, although the P and J pickups have their electronic differences.