I don't know about large objects like cars having thrown up that high into a supercell by a tornado, but it might be possibile particularly if the tornado was a large and very powerful one, say, about at least F5.
A stormchaser (I think it was Gene Moore) once said in his website that a tornado he observed had a car come flying out of the side of its parent storm at 15,000 feet.
Tornado-generating storms can still be be extremely dangerous for any commercial flight even if they don't drop a tornado. They are also known as supercells because they can last much longer than ordinary thunderstorms, often up to several hours. They're known to reach up to 60,000 - 65,000 ft. (one over Brisbane, Australia went up to 77,000 ft.) Which is amazing, considering that most commercial flights do not go above FL 410 - 430!
Supercells also generate hail up to the size of grapefruit, which'd be very damaging ,esp. to engines and cockpit windows. And they can produce some incredible lightning. Last, but not least of all, are microbursts, which are powerful blasts of cooler air that come rushing from above at speeds up to 100 mph (94 km/h) or more. Microbursts (also known as windshears) have been known to cause serious airplane crashes, like the Delta L-1011 which crashed during a thunderstorm in DFW in the late '70s. (damn, can't remember the date right now) They are highly dangerous, as they can be invisible to the naked eye. This is why aircraft today are equipped with windshear warning radar, which detects small debris and dust being whipped about by microbursts.
All in all, Ilyushin96M's right. Flying pot, pans and tires are the least of pilot's concerns where supercells exist.