I have an "emergency rain poncho" in my kit. It's been unused since I put it in there in 2005 (not sure if it even unfolds anymore). I doubt you need more than that, but you can always check the weather the day before you leave to get a better idea of what to expect.
It's a camping trip in the desert, not the redemption of the fallen world - Cryptofishist
according to legend, in the monumental rain of '98 you couldn't move. Playa dust doesn't turn into nice squishy mud when wet, it turns into gluey slippery slime. If it rains, you want to sit tight. So I'm told.
The 1998 rain event became absolutely ghastly and septic after only a couple of days. Took two years to clean up, and you can still see the mud tracks etched in the playa. So yeah, bring a raincoat. And a bucket or two.
I am glad I brought a rain coat in 2010 as it rained on Monday. I could have easily made due without it but it ended up working out as a pretty sweet and immediate accessory. A moment of Playa magic then occurred when the double rainbow dazzled the city! So yes, in my opinion, bring a rain coat, just in case.