I did the GDMBR this summer with SKS Shockblade front fender and a SKS Mud-X down-tube "shield" on my hardtail. I jury rigged a plastic sheet under my rear rack to serve as sort of a rear fender. My partner had Planet Bike full fenders (Cascadia?) on his rigid 29er. Both of our drivetrains stayed much cleaner than those in our "extended" group who had no fenders. Our clothes and sometimes our shoes would be spared too. I have to admit, however, that full fenders work better and they never clogged with mud - despite my expectation from the get-go that they would - not even with the "wheel sucking" mud of New Mexico.
But mud is not what you worry about on the GDMBR. Cow poop in quantities unimaginable; in all colors, in all textures, in all stages of decomposition. There is also elk and deer poop, bear poop (both black and grizzly), and in the Great Basin even antelope poop. It seems as if animals seek out roads to do their business.
Through New Mexico there are hordes of locusts that one eventually tires of sparing: instead one runs right over them, their carcasses forming roostertails - but for the fenders.
But as for rain and mud, from July 1 to August 24 we had only a few days of rain, but it was sometimes torrential. But because of the poop and locusts there is no question that when I do the GDMBR again I will bring full fenders.