When you copy from InDesign using the type tool, and then paste into Illustrator, you lose formating.
When you copy using the direct select arrow from InDesign and then paste into Illustrator, you maintain format but each word is a separate unit.
Is there a way to save formatting AND have have the text flow all in one unit?
I don't think so. ID uses a much more sophisticated type setting and rendering engine and therefore it's logical that AI would reset/ omit features it does not offer.