It would definitely increase output as the poles got closer to the strings... but it would also increase the likelihood that your fingers will push the strings into the pickup poles - making loud clacking noises - while you're playing.
I don't know, I just prefer the wood covers myself and don't think it detracts from tone in any way. But there may be some folks with super sensitive hearing that can detect differences.
It's good you can have it either way!
For me, exposed poles are aesthetic, they look BEAUTIFUL, but I have my doubts about them affecting the tone of a bass compared to the tone of full wooden pickup covers.
If pickups were microphones picking up SOUND, then absolutely exposed poles would sound different.
In that scenario, wood pickup covers covering the pole pieces would be the bass equivalent of having a pop filter between your vocalist and the mic — only the bass tone would be more muffled because there wouldn't be holes to let air pass through.
However, magnets don't pick up sound, they *create* sound — in conjunction with the vibrations of a metal string.
The vibration of the string is affected by makeup of the string, the age of the string, the wear and gunk on a string, the bridge, the body woods, the shape of the neck, etc.
That vibration then interacts with the pickups which are magnets creating a signal that is affected by the winding of wires inside and other internals like a preamp, if present.
Putting a wooden pickup over the pole pieces don't change the tone characteristics of the vibrating string, or of any of the electronics downstream.
The only thing I could see possibly being affected is the strength of the signal, but that seems unlikely — and if it were happening, an active preamp would boost it.
But hey, what do I know?
I thought Milli Vanilli was really singing those hits of theirs in the 1980s!