Is using the Magic Mouse 2 & original Magic Mouse on the same Mac unsupported in High Sierra?
I cannot find any Apple documentation stating that the original Magic Mouse is unsupported in newer OS versions. 

Your problem is more likely to be just one of Bluetooth connectivity. Apple provides a troubleshooting document that describes the Magic Mouse and Magic Mouse 2 together. Other remedies for problems can be found here.

The Magic Mouse is not one of Apple's strongest designs, and you may prefer a third-party mouse, or the Magic Trackpad, which I find much better. (You can leave it plugged in while using it, for starters!)