As kodiakbeer pointed out, even if this law had been in effect, this guy would still be able to buy the rifle legally because he did not get put on the no-fly list until after he tried to blow up Times Square.
Pretty much the only law that would stop him from buying a firearms is one that would stop an American citizen with no criminal history from buying a firearm - while I'm sure that such a law would please the Bradys immensely, it isn't a law most Americans will support.
Second, there is the effect Peetzakilla pointed out - if a terrorist wants to know whether the government is watching, all he needs to do is try to buy a firearm. Denial means he is one of almost 400,000 people in various terrorism related databases.
Personally, I think this is all just kabuki-theater. We already know from Heller that the right to own a handgun in your home for self-defense is a fundamental right expressly protected by the Bill of Rights. As such, even under rational basis, you cannot deny it to people without due process. Which means the Supreme Court would likely overturn it and the Administration will use it as a talking point to try and win points with people who get their entire education on an issue in 30 seconds - "The Supreme Court says terrorists can legally buy guns! Can you believe that?" After all, if you have a big nomination fight coming, you want people to be motivated to "correct" the problems on the Supreme Court...
Imagine if the media could lose their First Amendment right to blather cluelessly if they were on a secret terrorist watchlist and there was no appeal to such a decision. Would anyone think that was OK? Would we see U. S. Senators proposing such a bill? Yet despite a long, long list of national security problems created by ignorant media with free speech rights, some of which have no doubt actually killed people, we don't do that.