A few western states such as Utah, Nevada, and Oklahoma have passed laws making gold and silver legal tender, which is the premise these gold notes are playing on. The common sense assumption from this would be what you assume, that gold would now be accepted by the state government and banks at spot in payment for debts.
But according to
this article on CNN Money, it actually mostly affects tax on precious metal assets. It's honestly not entirely clear what effect if any this has on US gov't minted gold and silver eagles, since those were legal tender before and still are, though only at face value.
This article on money laws seems to affirm this; that essentially there are no taxes for the exchange of gold and silver as they are to be recognized as currency, not assets. This does permit precious metal to be a viable form of payment on par with cash since there's no tax loss simply by making the transaction, but it does not appear that even the governments of those states will necessarily accept payment in bullion at spot.
It's also pretty clear that you can't force anyone to accept gold or silver as payment. As for whether any individuals would trade for such a thing, in those states or any other - obviously not at most stores, no. Private individuals might negotiate for it the same as for any other verifiably gold item, especially if you're silly enough to offer it at face value (well below what Goldbacks sell for online).
