This is a bug I can't seem to pin down, but sometimes the import save function will glitch out. When it happens pressing "Load" will fail to remove the import menu. However, the two saves will merge in a way that seems to add cookies from one into the other, while not removing things like buildings or wrinklers.
Here's another related glitch I found while testing out Fanciful Dairy Selection. I ascended and purchased the upgrade, but imported the past save without bothering to close the dairy selection menu. In the new save I was able to select a fanciful milk. When I closed the menu, however, it refused to open again.
Other menus (Santa, Krumblor) can be left open while importing a save and won't be re-drawn, but they'll be nonfunctional.