No. They're trained on the data, but there's no point in training at which they go through some exercise that involves creating copies of some of their input using the model being trained.

In any case, why is it "a bit tough to say this"? You thought your ability to learn was irreproducible?

You're right that I jumped the gun and the analogy is not accurate. The point where they are similar is that you have the prefix as context as you try to type out the next word; it is a more deliberate form of reading, and when you do this there's an element of anticipation and analysis as you write each word. It's not quite the same as constantly trying to guess the next word, in my mind the elevated way of thinking was close, probably as close as it's humanely possible, but the analogy does break down there.

On the other hand, you can embrace all this and still let others weep about humanity a little.