Or will they just climb up into the rich soil and continue to spread? I do this already on a small scale by making compost piles with branches, etc. Then I just keep sifting out the largest branches until they are incorporated into the soil. But this is a terriffic idea! I guess the important thing is to pack all the air spaces and crevices, or at least the largest ones?

Sorry for the delay in replying. I don't believe that a hugelkultur mound will be enough to smother difficult weeds like this. They'll just grow right up through the layers of soil. Maybe if you cut them down first and then covered them with multiple layers of thick cardboard first, that might kill them.