I don't spider rig, but I have fished around bridge pillars. Main method I use is casting a jig down the sides and across the ends. Another effective method is Vertical Casting a jig, down the sides of the pillars ( Crappie.com - Crappie Fishing Information and Adventure - Vertical Casting )
Generally speaking, the Crappie will be using the pillars to hide from the current (if there is any) ... and will school on the down current side of the pillars. They will, however, come out a little ways from the eddy, in order to snatch a passing meal. So ... considering that both the methods mentioned have produced for me, in the past, I see no reason why a spider rig setup would not work. But, you'd have to make a few passes, in order to find the depth they're holding at ... or ... use one or both of the methods mentioned, to find that depth, then S-rig by the pillars.
Even while using jigs, I have been known to also use a second rod ... slip float/minner setup ... and let it drag alongside, between boat & pillars. The slip float setup allows for enough time to lay down the casting rod, as opposed to using a tightline setup (where, upon seeing a rod tip bend down, one has to pick up said rod while trying to lay down the other :p ).
.. cp