If you imported an Illustrator (AI) file into InDesign, it would be artwork which can't be edited.
It's not possible to share files between InDesign and Illustrator. While they share some of the same tools, they store their files in totally different ways. Importing art from Illustator to InDesign is limited. Only plain text can be copied because they have different text engines. Small pieces of vector art can be copied from one to the other, but only in a limited fashion which wouldn't work for what you're trying to do.