Due to differences in the type engines, I suspect you won't be able to do this via copy/paste.
If you really must get it into InDesign, the alternatives would to Place each Illustrator artboard on its own InDesign page, or save the Illustrator file as PDF and place that; then output the booklet from InDesign.
However, if by "to send to the printer," you mean a commercial printer, (as opposed to an office printer), there should be no reason to go to all this trouble. Just save the Illustrator file as PDF and let the printer handle imposition.
Firstly - Illustrator was not the correct tool to create a 32 page catalogue.
InDesign should have been used from the start.
Secondly - you shouldn't have to create the booklet - that's the printers job. Even when I was in prepress we would have someones send 1000s of single page pdfs. It was no hassle to put all these together and make a booklet.
Thirdly - you could just PDFs of your Illustrator files and then use Acrobat Professional feature to Combine Files.
Fourthly - if you really had to you could File>Place all the documents into InDesign. Then make a PDF from there.
You'd still require Illustrator to edit the files.