It shouldn't cause a problem, however, over a long period of time the magnet wire might corrode where it touches the magnets, causing the pickups to fail.
This all depends on whether or not they insulated the magnets from the wire (and some newer Jazz pickups have plastic bobbins where the wire doesn't tough the magnets) and it takes a very long time to happen.
But I wouldn't sweat it.

Just try and wipe the pickups and bass dry after you play it. A little clear nail polish on top of the magnets can't hurt.