All I can say is, if it does it is weak. I mean, getting stuck on level grass outside the stealership? That's pathetic. There was a very small dip under the right front tire, but it wasn't in mid-air, not even close.
I had a similar experience with my 2002 Subaru WRX. Subaru is known for AWD, and they make some good systems. They also make some lame ones. My 5MT WRX has a viscous coupling unit (VCU) in both the center and rear diffs. The problem is, they do not transfer much torque.
I first realized there was a problem when I got stuck (OK, not really stuck) on our driveway because the 2 rear tires were on ice and the 2 fronts were on dry pavement. "From the wheels that slip to the wheels that grip", right? Not so much, actually the exact opposite. The rear tires spun and the WRX actually rolled backwards!
After that, I did some makeshift tests at home, including one where I placed a 2x4 flat in front of the front tires and jacked the rear end up off the ground (using a floor jack). Then I attempted to drive over the small 1-1/2" obstruction. Nope. The WRX kinda tried but couldn't go over the board.
I took it to the dealer I bought it from, hoping they would find something wrong. When I told them about my test, I could tell they didn't believe me. They got a brand new WRX of the lot with the same AWD system off the lot and recreated my test in their shop. The new WRX failed miserably. The dealership also sells Fords, so of course the Ford techs got a big kick out of it.
The bottom line is, all AWD systems are not created equal. Some are very good, while others are little better than one wheel drive (1WD). Just because there are stub axles going to all 4 wheels does not mean a vehicle has true AWD or 4WD. Most "4WD" trucks with a transfer case and low range are really 2WD -- one in front and one in back. There are very few _true_ 4WD vehicles. Traction control has become very popular, and it works to an extent, but it's not the same as a good AWD or 4WD system -- because it relies on braking the wheels that begin to spin. So the brakes are being applied when you are trying to go forward, and in off-road situations, or on snow & ice covered pavement, the brakes can overheat. Then the traction control shuts down and you have...1WD.
Buyer beware. IMO, vehicle mfrs should be required to put the _actual_ minimum number of drive wheels on the window sticker.