It's pretty evident. Its training would no longer be anchored to reality, and given its output is non-deterministic, the process would result in random drift. This can be concluded without having to test it.

Now, if training was modified to have some other goal like consistency or something, and with a requirement to continue to perform well against a fixed corpus of non-AI-generated text, you could imagine models bootstrapping themselves up to perform better at that metric, alpha-go style.

But merely training on current output, and repeating that process, given how the models work today, would most certainly result in random drift and an eventual descent into nonsense.

It might have different effects over time. E.g. in the intermediate term it emphasizes certain topics/regions which leads to embodied mastery but over the long term it ossifies into stubbornness and broken record repetition. Similar to how human minds work