No, you can't wear paddock boots and chaps at shows. I know chaps are more comfortable than tall boots but I don't think shows allow that. If you're not sure then check the rule book for the show. Even if you were allowed to wear chaps I wouldn't because tall boots look a lot more professional.
Hope this helped!
I've worn half chaps at a rated show before. My tall boots broke right before my jumper round and I had to wear my chaps. Nobody is going to penalize you but it just doesn't look as nice, especially at a rated show.