Popovers seem to have scroll bars, albeit ones that you don't see. I created a large popover that exceeded the dimensions of my screen. I put text in the bottom of it and opened it up in browse mode. When my cursor was over the popover, I could scroll up and down with my mouse wheel.
This is true when a popover is created and is actually shorter than the content.
Interesting! Most of the small screens are on lap tops without a wheel, but I see the up and down arrow keys work