I also did the White Rim trail, 96 miles in four days, with a guide/support truck from Rim Tours.
I think the described sand would be a drag to deal with on a tandem, but doable.
As a mountain-bike challenge, it isn't too technical, but I was on a fully suspended bicycle. The technical bits are mostly shorter, up and down hogbacks where the trail can't follow the canyon edge. Therefore, even if the loss of traction due to loose surface meant that I had to just let loose and ride it out, the speed buildup was manageable.
If you do a four-day, there's one outside turn on day three, down one of the hogbacks, where missing it has you tumble down a shale slope. Even the guides walked their bikes.
The big questions in my mind are:
1) Have you and the stoker ridden the tandem on reasonably challenging fire-roads? Depending on season and time since maintenance, the White Rim is about as bad (in short stretches) as fire roads get and still be SUV navigable.
2) Is it acceptable to you to walk the bike up and down some of the hogbacks?
3) What's your support situation? We went in September, but had unseasonably hot weather. Our crew drank >1.5, almost 2 gallons of water per day per person, more than they planned for. The guides were going to have to drive out and get water after making camp on night 3, but fortunately one rider caught his wheel in a gully, flipped, and broke his wrist. So they could fill the waterjugs while doing the hospital trip.
If you consider four days, two people, 2gal, that's 16 gallons of water, so 128 pounds. I've always thought that an unsupported trip would have to be a two-day trip.