Pickups can range from virtually non-microphonic to slightly microphonic to extremely microphonic. For a pickup to be microphonic, internal parts have to be able to vibrate in response to external vibrations. Soaking a pickup in wax or epoxy ("potting") will reduce those internal vibrations and make a pickup less microphonic. As pickups age and parts shrink or loosen up, they can become more & more microphonic.

Microphonic pickups will feedback at higher volumes, and it's not the musical sort of controllable feedback -- it's a nasty squeal, like pointing the singer's microphone at the PA speakers. The more microphonic a pickup is, the more sensitive it is to volume, distortion, and compression. But at lower volumes, microphonic pickups add an airy spacious acoustic quality to the tone.

Early Gibson humbuckers weren't potted. Fenders were dipped in either wax or lacquer, but they weren't deeply impregnated and they were very prone to loosening up with age. Deep potting didn't become common until the late '70s/early'80s, when the older pickups were shrinking and squealing, and higher volumes & more distortion were exacerbating the problem.

If you rock out at high volumes, microphonic pickups are bad. Clean, or at lower volumes, slightly microphonic can be good. All the best PAF replicas are unpotted, many Strat/Tele pickups have shallow old-style potting. But all of the best modern "hot rodded" pickups are deeply potted. In general, humbuckers are more tolerant of being slightly microphonic and you almost never see completely unpotted Strat/Tele pickups.

Lenny is reputed to have pickups that have loosened up and become somewhat microphonic. Stevie only used Lenny for his cleaner, quieter, "prettier" songs like "Riviera Paradise" and (of course) "Lenny", and you can hear that it had a haunting, complex, unique clean tone. But he also used cleaner amp settings, and there were lots of other things that contributed to Lenny's tone (brass saddles/nut, maple fretboard, the only Strat he kept setup with the trem floating) so it's hard to say how much of that tone was the pickups.

You can make a microphonic pickup less microphonic by potting it. But you can't practically un-pot a pickup to make it more microphonic (that may happen with age -- shrinkage and heat cycling -- but it would be hard to intentionally replicate that).

edited to add (like it's not long enough already): Some of the boutique makers do intentionally duplicate shrinkage and coil loosening, by starting out with intentionally distorted parts and then winding the coil loosely. But you can't just heat up a modern-spec pickup and suck out the wax to create a musically microphonic pickup.

You might ask in the Custom Shop forum or the Ask Mike Eldred forum if their Lenny replica pickups were microphonic. (They hate to divulge details of the various Tribute pickups but who knows -- someone might be willing to share info.)

If you shout into a microphonic pickup you can make cool noises like this. (0:28)

http://www.youtube.com/watch?v=0D8GvpKsqd0

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Rated "M" for meaty.