I would prefer to add this to the original, in InDesign for example.
If it is not possible, Acrobat has a feature that allows you to access headers and footers to include page numbering, called Bates Numbering.
This can be done with a custom-made script. If the non-empty pages contain text then it can even be done automatically, without you having to specify which pages are blank and which are not. I had a look in the sample file you shared and there it would be possible.
Thanks for answer. Have you a script for it?
Like I wrote, this will have to be custom written for your purposes. I could create it for you, for a fee.
If you're interested contact me privately (click my username and then Send a Message) to discuss it further.