Two things:

1. The InDesign document doesn't have an exclusive CMYK or RGB nature, like Photoshop or Illustrator documents do. It can hold content and placed files of any origin and in any kind of color system.
2. Upon printing or exporting to a PDF, you can convert all content to the required color system and profile. So it's never too late to convert images. In fact, converting them before using in InDesign might be considered too soon. And even the printer staff can convert the images within the PDF, if necessary.

So: NO, you don't need to.

And if you're sending the InDesign document (in stead of a print-ready PDF) to the printer, then the operator can also set the proper conversion.

Oorspronkelijk geplaatst op Quora: Do I need to convert all the linked RGB images to CMYK, before sending an InDesign document for printing, if the InDesign document itself is CMYK?"