I think the print mode button is valuable. It provides an affordance that shows you you can turn of the GitHub notice and footer, and use this for actual invoices. Lots of people don't know about print-only style sheets, and how many people are going to print-preview the page as opposed to click a button out of curiosity?
I'd still keep a print button; not a enable/disable, but at least a button that triggers `window.print()`. "Print" buttons may seem useless, but they do serve as a simple bit of advertisement that "Yes, this page is print-friendly!"