No, not that I know of, at least not as I understand your question. I own both devices (and am very happy with them!) and also regularly switch between two computers on both, and I have not noticed any such function.
What is supported, however, is "Logitech DuoLink", which allows you to assign a function to mouse movements by pressing the Fn key.
What is also supported is Logitech Flow, but this is about using the mouse and keyboard simultaneously for two computers that are switched on and as I understand your question, this is not what you are looking for (but still a handy feature).
https://www.logitech.com/de-ch...