You can't open nor embed a PDF from any other application than Illustrator in Illustrator without destroying content. Illustrator is not PDF editor.
You can place and link a PDF/X-4 to Illustrator, you can save Objects in InDesign in a CC Library and use it in Illustrator or InDesign, you can save font properties and colors in a CC Library and use it in Illustrator, Photoshop and InDesign.
TEXT HAS NEVER TO BE OUTLINED IN INDESIGN DOCUMENTS AS IT CORRUPTS CONTENTS AND CAUSES A HUGE LOSS OF ELEMENTS!
Eugene, I'm assuming you're not trying to edit the ID exported PDF in AI right?
I can't find any difference in embedding vs. placing, so if you want the convenience of embedding there shouldn't be a problem. You can test linked vs. embed by saving different versions of the Illustrator file with the placed PDFs as PDF/X-4. When I do that Acrobat's object inspector tells me there's no difference in linked vs. embedded.
If your ID page has transparency you probably want to export as PDF/X-4 to keep the transparency live.
Embedding ist technically the same as opening and converting to the color space of the host document in one step. This causes problems in damaged text strings. It is not recommended to do that.
Placing as linked file keeps the PDF complete, similar as placing into InDesign. It keeps its original color space, no conversion is done.
When you save an AI file as PDF with embedded PDFs, all elements have the same color space, with linked files it is possible to keep different color spaces for different objects.
It's for packaging, so it's important that the outline is kept etc. and things are kept in tact.
Original files supplied in InDesign, and need it in Illustrator.
Resolved now though - as printer will accept PDFs.