I’ve never done it nor seen anyone do it IRL. But I believe it could be done, at least at the gate. A car is very heavy and has a lot of power behind it if it is going even 30 mph. Most metal on gates would not hold up to that hitting it. Especially when you think that all you really have to break is the one point…the hasp or lock of the gate. Once that is broken the hinges will allow the gate to open enough for the car to get through. But as @JLeslie said, it would damage the car too.
I’ve always wondered about the scenes where someone drives through a chain link fence, though. The design of the fence at that point is different than a gate. It is more flexible and spread out. Not hard and brittle. If a car hit it, I would think the flex of the fence would absorb some of the energy of the car. And the energy of the car is not hitting the panel of fence with the same energy. At the point of impact, lots of energy. Even 4 inches away and it is a lot less. And even if you tore the panel completely away from the fence, it is highly flexible and it seems like it would wrap around all sorts of things on the car. This would result in it being dragged, I would think.