Revision numbers are for the birds! John McGhie can refer you to an industrial accident caused by this practice.

You can't put it in the footer unless you want separate sections for each page. You can have continuous page numbering without any problem doing that. However, you will not have continuous text. Imagine that you add a 6 line paragraph to an already full page. You will get to move text from section to section to section to section... Not fun.

You can make it look like it is in the footer, though. To do so, use a textbox or shape anchored to the part that you change. Position it where the footer is. Insert your revision information. This will make it difficult to edit but not as difficult as a separate section for each page.

Consider using footnotes instead?

In some ways, the StyleRef Field might work out for you. You would have to put the reference number somewhere on the page itself for that to work, and remember to change it every time it changes.