Technically speaking once the missiles are unlocked you can hit the launch button at any time. There is no "software limitation" and that is sort of the catch.
The real question is, did you play the game until you got the real launch order? Did you launch the nuke?
This is what bothers me most, I fear that many will give up way before that. There are a total of 5 drills spaced 2 min apart, with the final order 2 min after the last drill. After drill 3 you get the alert message (sort of DefCon 3) and after the 4th drill you get a target update message. But I think that most people will be turned down by the waiting.
BTW, if you want to read the epilogues without waiting 15 min, you can read them at http://nlc.rioki.org/#/launch and http://nlc.rioki.org/#/nolaunch.
Thank you I will think about your input. I was thinking of implementing a "manual" that slides in from the side with more detailed instructions.