Can you plug a mouse into two computers? What happens if you do?
It's just a mouse and not likely to cause any kind of issues as you can plug two phones into one USB and the most that usually happens is the one with higher charge begins charging the lower charged device. Not always but usually. What I'm saying is try it.
Anyway, consider what you're asking. How would the device or the mouse know which click is for the left device and which is for the right device? Simply looking from one to the other doesn't tell the mouse which device is the focus of attention. So let's consider that a cursor appears on both screens and you scrolled up to something you wanted to open on one device the mouse is likely moving on the other screen as well and both will accept the same input so anything on the non-focus device will do the same as on the focus device. Again try it but it isn't likely to work well.
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