Depending on the design of the mouse, I would say it's technically possible. Is it worth the time for someone to figure out how to do it? Probably not, considering that every different model of mouse could be different inside and you'd need a different version of the virus to infect said mouse.
Why do you think viruses target Windows? That one of the few things you can count on being the same between almost every PC.
Again, back to the design of the mouse. If the mouse's flash is recognizable as a flash drive, it's probably going to be infected.
I have a cheap printer that has some on board memory that shows up like this. The printer uses it as a cache, but I could easily load that memory with whatever I wanted. I doubt that the mouse would have such a design, but probably there are a few out in the world built like that. Do you have one, I dunno, I would guess not.