Can I create a document in Illustrator without attaching to the notion of paper with finite size?
Can you DELETE the ARTBOARD?
I reduced the artboard to some small size and remainder drawings persist. Can I delete the artboard at all?
You have to have some sort of an artboard.
Illustrator places artboards on a canvas space, which is sized at 16383 x 16383pt. You could create a new document with those dimensions.
Or, you can go to
Hide Artboards (Shift+Ctrl+H) to just ignore whatever artboard you have defined.
Either way, be careful when exporting!