Illustrator support was right. It's not possible to open a .ai file in Draw as an editable file but, you can bring .ai files (and jpegs) into an Image Layer in the app; they just won't be editable. You're just not in the right spot to do that.
Here's how to add files from your CC Files folder to your Draw artwork:
1. When you open a new Draw artboard, you'll see a Background Layer opposite the toolset.
2. Tap the + just above it to open a pop-up menu with the choices Draw Layer and Image Layer.
3. Tap Image Layer
4. Then choose from where you'd like to import the image (your choices will be: On my iPad, Take a Photo, My CC Files, From Market, From [Adobe] Stock, Paste Image); in your case you want My CC Files.
Let me know if that helps. Also, let me know if I've misunderstood what you're trying to do.
Yes!! Haha, so much easier than I was expecting. Thank you!!
Oh good. I'm glad I was reading your post correctly; after I finished writing I started to second-guess my response.