Ok, here is the full story. I drove the car a lot today... Over 120 miles. This evening I had to drive a very long distance for a family gathering, and when I left home I only had 10 miles of charge on the battery. So, I put it into Sport mode for the entire 65 minute drive there. In sport mode with some charge remaining, the car performed just fine. It kept the battery at 10 miles of range and at 33% charge.
So, for the drive home I put it into Stealth mode and let the battery run out. When the range extender kicked in I noticed that the car had a very hard time accelerating at every stop light, so that's when I decided to get the camera out. It didn't matter if the car was in sport or stealth mode, actually. Both modes performed exactly the same when the battery was kaput.
The car was dangerously slow as the video shows. That was the first time I've had to run the ICE that long, so I don't know if it will behave this way every time, but we'll see.