Actually, no, when importing an Illustrator document as a Comp or creating a Comp from AI source footage later, After Effects does not see objects nor sub-layers as separate. AE only sees AI Layers and all AI layer contents are merged onto the corresponding AE Layer.
So, we've always had to move any Illustrator objects that we want to animate separately on the AE side to their own layer at the root level of the Illustrator document (that is, the object cannot be on a sub-layer). The "Release to Layers - Sequence" option in the Illustrator Layer panel pop-up menu can be helpful for this as it promotes each object on the selected Layer to its own sub-layer which can then be renamed and promoted to Layers.
Have you tried using Adobe XD yet to export to After Effects?
Export from Adobe XD to After Effects | 1 Minute Tutorial
You open the Illustrator document in XD (File > Open) and then choose File > Export > After Effects. With this approach, the Illustrator objects become AE Layers in a Comp. If you take this approach, be sure to review Supported features when you export to After Effects from the Adobe XD User Guide. What's not listed here that probably should be is that the Illustrator document Layer structure is not supported. If I could make any change to how exporting to AE from XD works it is that the AI Layer structure would be maintained via AE Comps and pre-Comps on the After Effects side. That said, Groups, Artboards, and Text Layers are supported.