Hi Loic,
I think it’s quite possible. You can do this using BridgeTalk message object (don’t confuse it with Bridge application). You can get detailed information about it in the “Interapplication Communication with Scripts” chapter in JavaScript_Tools_Guide_CS3.pdf.
In illustrator you can unlock all layers and objects, remember parameters of the document you need: page height, page width and so on, then select all objects, copy. The in InDesign create a document using the same height, width and so on, then paste, save and close document. But it will work, if illustrator documents consist of quite simple objects, otherwise the objects will be pasted as one PDF object into InDesign.
I made a few scripts using inter application communication e.g. InDesign and Photoshop, but I’ve never made scripts for Illustrator, because don’t use it often. Debugging of such scripts in JS is a little difficult – in AS and VB it’s done much easier. If you are interested, you can read a good book with a lot of examples – Adobe illustrator scripting by Ethan Wilde – but it doesn’t cover JS – only AS and VB.
Kasyan