Here is one way, You will need to open each Illustrator file, duplicate the original layer and call it "Outlined type". Go to select> Objects> Text objects, then Type> Create outlines. (outlined type won't be recognized as words, unless you ask it to try).
Open your InDesign file, select each linked Illustrator file and go to Object> Object Layer Options, turn on the outlined type layer and turn off the original layer. Keep the original Illustrator layer, in case you need to make future edits.
Thanks very much for your reply and detailing the process very well.
I have tried one and tested it in both Preview and Acrobat. I have 101 images to do but your process is very fast so shouldn't take long at all.
You are welcome. I don't think Acrobat can count the words, but it will read them to you, which is fun. (View> read out loud.) FYI, Preview sometimes does not give a completely accurate representation of PDFs.