I believe the Corvette Museum will be able to repair the damages caused by the sinkhole. More than likely the Corvette Museum had insurance on the building, as well as the cars housed within. When considering this, they shouldn't have a problem recuperating for the sinkhole that opened up under their property.
Yes, this museum is very popular, and has made a lot of money. Because of this, they will have the money and resources to repair all of the damage that the sinkhole caused, and I do not think that any cars were destroyed that are completely non replacable antiques cars.
The Corvette Museum will be able to repair the damages done by the sinkhole because there is a lot of financing behind the museum. The corvette name and corporation represents a higher level of income and consumerism and the money available for repairs will flow in. Also, the media exposure will almost guarantee this happens.
Things are just things. That's what people without things say. Own a corvette, and you will understand why they are not just things. Own a collection of the rarest corvettes around, and losing such a collection is devastating. Even if the museum is rebuilt, and the cars repaired or replaced, the damage has been done. Some of those corvettes were more than just what came off the assembly line. The history of the metal becomes the true value. A corvette featured in a stunt or a movie are one of a kind. There is only one car that ever achieved whatever it was, and now that car has been destroyed. A bit of history is gone.
Sinkhole damage to the Corvette Museum is unfortunate but the damage cannot be repaired quickly. Sinkholes are unstable and because of this, the whole area is in danger of getting more damage. Repair crews would have to wait many days to make sure the area is stable enough for repair but that would take many months before it starts.