Whether it's presented as real seems a reasonable line to me.
Fox News could not use it to mislead people into thinking Biden said something that he did not, but parody like "Sassy Justice" from the South Park creators (using a Trump deepfake) would still be fine.
It doesn't have "memory" of what it has generated previously, other than the current conversation. The answer you get from it won't be much better than random guessing.