First off, no they cannot examine this deck. Of course not. But then again, if you present this
correctly at the beginning they would have no reason to want to. You apparently freely show both
sides of a completely blank deck, have the spectator name a card and have it appear as the only face
down card in the deck. There is no complicated memory work involved (minor memory work, yes, but not
complicated), and reset is relatively quick and easy. Any card can indeed by named, and while you
could immediately repeat the effect with a different outcome, it would be a mistake as the
spectators would come to the obvious conclusion that you are using a trick deck rather than just
having the card they wanted in there.
This could also technically be used as a new "out"
for your performance rather than using an Invisible Deck. It would rob the true intensity of the
effect, but it would definitely set you apart from what they might have seen other magicians do.