It is certainly possible to convert animated cursors (.ani) to (.ico), but what this export actually does is that it saves one of the frames from the .ani file and produces a static .ico file from it. Which means that technically, you can have several icons made out of single animated cursor, which is what ani to ico conversion represents. This is similar to how icons are made from animated gifs for example. You can find various icon editors and converters for this.
Updated: March 9, 2023