Come on, it'll be fun. Just for grins, I asked Google to plot a route for me. It wouldn't do the whole thing in one fell swoop, and even for short distances (like Singapore to Bangkok), it suggests flying. But giving it one piece at a time, it manages to cover the entire route. It did have some trouble crossing the border into China, but we got around it. Of course I don't know if this is the route Mr. Crazy Man took, but it shows that Google at least thinks there are roads that go all the way.
There are two base camps at Mt. Everest, one in Nepal and one in China. There is a road to the one in China. There don't seem to be any roads to the one in Nepal. Matter of fact, it looks like the only way in or out is via air.