Falling over on carbon frame bike -- likely to cause damage?
In practice, there is one thing I've seen enough to call it a pattern: aero/teardrop carbon seatstays and chainstays cracking near the joints after being flexed excessively during a crash. Some of these combine very light construction with a very flat joint in the side to side direction. Some frames like this you could probably break by falling over at low speed enough times. I'm mostly talking about the kind of tubes you'd see on a tri bike.
Most carbon bikes have nothing like the above vulnerability and, falling over at low speeds, realistically would only get damaged in a major single point impact to a tube. You could probably get that to happen if you fell on the wrong thing.