Not likely, according to S&T contributing editor Fred Schaaf. In the January issue of Sky & Telescope he writes: "Unfortunately, the planet’s glare and scattered light in a telescope will hide the dim nebula. Saturn’s surface brightness is 250,000 times greater than that of the Crab, which is 6 by 4 arcminutes in size, nearly 10 times wider than the length of Saturn’s rings."
Rick Baldridge, a member of the International Occultation Timing Association (IOTA) disagrees. In the Peninsula Astronomical Society [California] newsletter for December 2002 he states: "It doesn't seem so far-fetched to see a 0-magnitude planet near an M-object. Back in 1982, I saw a 4-day-old Moon pass between the Lagoon Nebula (M8) and the Trifid Nebula (M20) using a 5-inch f/6 refractor with a 20-mm eyepiece (about 38x) and a nebula filter. I was astonished that with that much moonlight, the nebulae would be visible, but they were. I think it will be rather easy to see Saturn transiting the Crab Nebula — with the use of a nebula filter."But why not take a look to be sure? The passage of a planet across a nebula is so rare that few observers have ever witnessed such an event. Saturn will be in the middle of its traverse across the Crab at roughly 23:00 Universal Time (6:00 p.m. Eastern Standard Time) on the 4th. Perhaps a more interesting observing challenge will be following Saturn's largest moon, 8.4-magnitude Titan, as it makes its way across M1 during a 24-hour period beginning at approximately 2:00 UT on the 5th. Note that Titan will pass only 20 arcseconds north of the Crab's central pulsar at about 14:00 UT on the 5th.
And how close to Saturn can you detect the Crab Nebula? You can easily locate its position for a week or two before and after January 4th by remembering that Saturn is moving westward against the stars by about 4.5 arcminutes (6 ring-lengths) per day.