Out of curiosity, what is this circle test? I grew up in CA but didn't start riding until I moved to Texas. The test here doesn't involve a circle, though there is a "figure 8" box involving tight turns in both directions. I imagine it serves the same purpose.
On the ease of testing on a dualsport/light bike...
Here in Texas, you can take the MSF beginners course instead of a riding test at the DMV. The companies giving the course are licensed to administer the same riding tests that the DMV would give, so the only real advantage is that if you dump it, you don't booger up your own bike.
A few months ago I retook the MSF advanced course after I bought my Sherpa. The figure 8 box that seemed so tough before on the school's Rebels was a breeze on the Sherpa. I was laying into the turns FAST, leaning my body inside of the turn and clearing the narrow sides of the box by 3 feet. The instructor finally suggested I should try counterweighting. I guess he'd never had anyone take the advanced course on a 250 pound DS bike. I went ahead and hit the box counterweighting, but didn't turn any tighter. He said "Uh, well, ok, now you know there's another way to do it." We had a good laugh over that.