Yes, a high-downforce race car, such as a Formula 1 or Indy car, can produce several tons of downforce at speed, so it is literally possible for one of these cars to stick to an inverted track.
However, road cars are a different beast entirely. For practical reasons, they simply can’t be built to fully utilize the ground effect. The best most street-legal road going cars can do is minimize lift. I’m not familiar with this particular model of Ferrari, but I seriously doubt their claims.
Doing some quick back-of-envelope calculations, a three-inch, five-foot wide wing on a car, assuming standard sea-level conditions and a very generous C[sub]L[/sub] of 3 (if it’s not some huge multi-element rig, it’s almost certainly much less than that), would produce 464 lbs. of downforce at 220 mph. I don’t know what the body is doing, but it can’t be producing much more than a couple hundred pounds of downforce itself, and most likely is actually generating a little bit of lift.
Therefore, I would guess that the car has no more than 600 or 700 pounds of downforce total. Since the curb weight is probably around 3,000 lbs., it would not be able to stick to an inverted track. I wouldn’t believe any claims that a street car could generate that kind of downforce without seeing some wind tunnel data.