That sounds like a different situation than @MEB was describing. He really was talking about importing AI documents where the AI document has items that are outside the artboards.
For documents you create In AD, you have a choice of having an Artboard or not (in which case you have a Canvas).
If you have a Canvas, and you drag an item off of it, its visibility is controlled by the current status of View > View Mode > Clip to Canvas.
However, if you have an Artboard, objects that you drag completely outside of an artboard will always be visible. Objects that you drag partly outside an artboard will be partly visible.
