Let's say the following scenario occurs. A quarterback throws a screen pass, and the player drops it. There is a whistle for an incomplete pass, and a player on defense grabs the ball and returns it for a touchdown. The coach of the team that was on defense challenges the ruling on the field of an incomplete pass, and it is overturned, because it is ruled that the ball went backwards. I am almost sure that the touchdown does not count, but does the fumble recovery count? What about if the player on offense hears the whistle and doesn't try to get the ball? Is there a clear rule? Is this a judgement call?
If the whistle blows without a recovery the play is dead. Now there are certain bylaws outside of the NFL that allows for reviews to anoint the probable outcome - meaning a player picking up the ball in this situation would have clearly picked the ball up with or without a whistle.
In the NFL a player could be awarded the ball in this situation too. If the whistle blew while he was in the act of retrieving the ball (and referees have been liberal with this to fix bad calls) they can award the player the ball but however he cannot be awarded any return yards.
You hit on a really keen and obscure point that really is kind of kept under wraps in the NFL. The media, the broadcasts, everyone... is really not questioning when a whistle was blown on a play or trying to scientifically call out an official. Who knows in 3 years we might get close-ups of the ref's showing their cheek movements of when the whistle started going frame by frame with the action on the field. Until then NFL referees are going to probably be extra liberal in awarding challenges when they where deserved. You have to realize that in the situation you are describing the ref messed up and the team gaining the turnover gets no yards. Penalizing them further by not allowing them the turnover is egregious and could easily determine a game. So to answer your question the whistle marks a play dead. There is no way around this if it is clear. If the whistle is not clear then replay can decide whatever.