This first generation of Chatbots usually writes in a very generic way, unless told to do otherwise. By default, results are grammatically correct, sentences are well balanced, and paragraphs do a good job of introducing and structuring ideas.
But Chatbots usually don’t sound like any particular person. I suspect that this is deliberate, based on their intended use. If you are going to use a Chatbot for information retrieval, maybe you don’t want it to sound like your Aunt Edna from Brooklyn.
But the uses of Chatbots will inevitably expand, and sooner or later it may become more common to have them imitate personal styles of speech. The result might not be as grammatically correct, but it will seem a lot more human.
The question is not whether this is possible (it certainly is), but how it will be received. It is not clear how people will respond to being spoken to on a regular basis by computers that imitate the real people they know.
Will it be the next Google? Or will it be the next Clippy?