Yes, that's exactly how it should work. Same as a Chip and PIN card.
We developed an NFC-based protocol that does pretty much exactly what you've described (uses a POS terminal not an app for security reasons).

Final version to be released in dec. Let me know what you think: The (draft) white paper is available for comment at <!-- w --><a class="postlink" href="http://www.opencxp.org">www.opencxp.org</a><!-- w -->

The NFC ring is[i:noazjxgj] ideal[/i:noazjxgj] for bitcoin. It was just waiting for the right protocol...

Noticed your product in the press while I was working on exactly that over past few months (openCXP) so I even made a mention of it in the draft white paper. Perfect fit. Draft is available for review below if anyone would care to comment:

<!-- w --><a class="postlink" href="http://www.opencxp.org">www.opencxp.org</a><!-- w -->

Currently soliciting any feedback/comments from those interested in the fledgling cryptocurrency POS and ATM industry - final version should be avail early dec.