I don't know of a way to preserve the styles. And copying/pasting text from Illustrator to Indesign results in text converted to outlines. But here is a way to at least preserve text formatting from Illustrator to Indesign and retain useable text.
Save Illustrator file as PDF. Open PDF in Acrobat, save as Rich Text Format. Import rtf into Indesign.
I'm assuming your reply of "Yes" is that you can retain styles from Illustrator to Indesign.... if so, how is it done?
I've only replied to the question and I don't say "Yes", I say "Yes...".
That means that you can copy text from AI and paste it in ID preserving what you have in AI, but... depends on what you want really do with this.
If I have to do it, I'll use your proposal! More interesting!
As InDesign has a complete different text engine as Photoshop and Illustrator have (both have the same), it is impossible to do it in the simple way.
But because an AI file is a kind of PDF you could use 3rd party converters like PDF2ID PDF to InDesign CC, Convert PDF to InDesign CC, Open PDF in InDesign CC.
That wasn't going to be helpful in my project, but it's a good workaround the different engine issue Willi confirmed. Thanks!