I think one could drive to the top of the pass and back. There are two things to consider about a vehicle on a 4x4 road. What is the width? A 3/4 ton pickup is 6" - 8" wider than the normal SUV. Doesn't seem like much, but when passing a vehicle going the other way on a shelf road, it can get interesting.
As for ground clearance, it's not just how much spacing is under the axles. Vehicle length must also be considered. Don't know what your truck configuration is, but you can imagine that a crew cab with an 8' bed will hang up on a lot smaller obstacle than a short bed standard cab.
If you decide to do Ophir, the tricky part is on the west side of the pass. There aren't many good passing places for a mile or so near the summit. If travelling east to west, stop at the last switchback going down and look for traffic coming up. You can see the road coming up around the amphitheater or bowl. We've sat there and waited for 15 minutes or more waiting for the traffic to clear so we didn't have to try to pass someone.
I've done the whole thing in our 96 4Runner. Taller tires, rear locker, pretty good 4x4 capabilities. (We notice that when one gets to the really tough trails, one sees Jeeps and Toyotas.) We went over the pass after it had snowed a little the night before. The section along the stream gorge just before the waterfalls was pretty extreme pucker with everything being wet with a skim of slush on it. :E