Your comments seems a bit tongue in cheek, but the answer is probably not.

This law doesn't protect works made for hire--and presumably the monuments would have been. It also only gives standing to sue to the author of a work, so the general public couldn't rely on it and if the author is dead the right to sue likely died with him/her. Finally, it doesn't prevent taking something down--only mutilation or destruction, etc. of an artist's work.

If I park a car illegally and claim that it's performance art, can I sue the city when it gets towed away?

"In a 2006 decision involving public sculptures that were removed from the park for which they were created, the United States Court of Appeals for the First Circuit ruled that VARA does not protect location as a component of site-specific work. VARA covered works can be moved as long as the move does not constitute 'destruction, distortion, or mutilation.'"

https://en.wikipedia.org/wiki/Visual_Artists_Rights_Act

In this regard it would matter a lot whether "taking down" means a destruction of the monument/statue/sculpture or simply removing it from that location to be put in a box somewhere out of sight.

I suppose most confederate monuments are not copyrighted, unless they have been created after Mickey Mouse.