The ground plate in a Tele has a great effect on the bridge pickup. I took two sheets of clear plastic, put a tablespoon of fine iron filings between them and taped the edges.
I placed a guitar on it's back, and slid the sheets between the strings and pickups. I was curious how a ferrous or non ferrous bridge plate affected the bridge pickup pattern, and the effect the copper PLATED steel plate had.
I went to the nearest Fender dealer and checked several Teles. The plate alone, in a non ferrous bridge, extended the pickup pattern about an inch toward the neck pickup and to the saddles. Without the plate, the pickup pattern was quite narrow and focused...like a Strat.
A ferrous bridge extended the pickup pattern further, up to the neck pickup actually and past the saddles, albeit quite weakly the further from the pickup you go.
Now, that's with a STEEL plate. (the copper is just plating to aid in soldering a ground wire to it, and to help prevent rust.)
The copper plate of the P pickup is copper, not steel, so it's effect on the pickup pattern won't be what steel would have. Since a P pickup is humbucking, the shielding of the plate would have minimal effect on that. A steel plate under the pickup would be interesting, but I'd expect some weird problems with the A and D string pickup pattern, due to the polarity differences between the two coils.
BUT in a Jazz bass with single coils, a steel plate would be very interesting...
BTW, a steel plate is not recommended for stacked single coil sized humbuckers or side by side coils.