It is not possible out of the box.
But with scripting or with 3rd party plugins.
I'm currently using a 'batch process' in Acrobat Pro on all my Print PDFs (to convert to online PDFs). Guess I'll stick with that then.
Was hoping there would be something magic I could do when making the original PDFs from InDesign.
You can use MadeToPrint from Axaio or Output Factory from Zevrix to create batch processes directly from InDesign.