Yes! I have an old training video with Isabel Werth. (I know, controversial.) She is doing clean changes on a four year-old and the horse looks like a third level horse. As I mentioned upthread, I attended a young horse symposium a few years ago. The horses were all three and four, ridden by pros. They were all warmbloods and looked way more advanced in training than one would guess because of their age. Would these people show them at third or fourth level? No. Would being ridden that way enhance their sale potential? Probably yes.
Long ago, I owned a Lipizzan cross. I bought him as an unstarted four year-old. Three months after I started him, we showed training level and won, beating a nice WB stallion. Some horses are very precocious.