You would need to copy the Illustrator object and paste it into InDesign first, then check to make sure it's editable, such as test if you can change the fill/stroke and edit the paths with Direct Selection tool.
You may need to Edit > Expand in Illustrator first before copying over, and then in InDesign, Ungroup and/or Release compound paths if they exist.
Once you're sure it's editable, select the object and add it to the CC Library from within InDesign as a Graphic

In case you're not aware, InDesign graphics in a CC Library can't be linked to instances you place into layouts, you can only place copies. That's probably what you want, anyway, since you're looking for a solution where the users can edit the copies they drag into their layouts. (If you want instances linked to the original, use native Illustrator or Photoshop graphics in CC Libraries.)
AM