You can create a new document (without page numbers), then place the pages of the original into it.
To automate this, I think you should as over in the scripting forum: InDesign Scripting
There are scripts already for placing multipage docs, and I think someone may have written one to add the blank pages, it's a fairly common request.
If you export to PDF, Acrobat includes an Insert Blank Page function (which wouldn't affect the InDesign-generated page numbers, of course), but that would be a one-at-a-time proposition unless you can find a way to script it.
One at a time won't take long if you use the Pages Thumbnails pane to arrow-key navigate, and the keyboard shortcut to execute the insertion.
I do have several scripts that the wonderful people here (and in scripting) helped me with to do you what you want, BUT they do effect the page numbering. With the kind of scripts they are, I don't think that could be avoided. If you are interested in them, let me know.