Not by itself, but if you wanted to put an LLM into a personal assistant, you could teach it specific codewords and have some agent software that integrates with the email client scan its outputs for the codewords and trigger actions when they appear instead of outputting them to the textbox. Conceivably that could be useful, if you wanted to give an LLM the power to react to "Open a new email to Kate and in formal tone accept her invitation to the party she mentioned in her message yesterday" appropriately.
Now I wouldn't want that, but I think there may be enough techbros who would, that it could exist.