The sentence is (s odřenýma ušima) grammatically
correct, but no-one would say it. Why? Because crashing is not an
inevitable consequence of being driven too fast.The sentence is
defective semantically (= in terms of its meaning and topic
focus).
- What happens when a car is (being) driven too fast? It crashes. It might / could / may
crash.
Why „at a pinch“ (s odřenýma ušima)? Because the indefinite article
„a car“ sounds almost impossible here. Why? Because if it
was being driven too fast, we already know about the car.
Something was being driven too fast. What was it? A car.
- Because it was (being) driven too fast,
the car crashed.
- (more idiomatic): Because it was going too
fast, the car crashed. [We don't need to say the car was „being
driven“.]
So the short answer is: the use of the participle („being
driven“) is ok, but it's a sentence no-one would say. ☹️