Generally the kind of people who act on fatwahs to kill people like that are not super ninja assassin masters, but actually fairly incompetent. Being alert (which is one of the main things taught in self defense classes) would be a huge advantage, but in a place like the home, being armed would improve one's chances substantially.
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You don't have to be a super ninja assassin master, you just have to be hidden. Even walking behind the target is good enough, especially if you're happy not to escape.
John Hinckley Jr was neither particularly competent nor particularly sane, but he managed to shoot Ronald Reagan and not get shot himself despite the fact that Reagan was surrounded by quite a few armed guards at the time. And there was another president who got shot by some random bozo in a good hiding place, whom I shall refuse to mention because this is the internet and you just know it would immediately summon a horde who want to discuss their conspiracy theories.
Basically, if I had people actively trying to assassinate me, the simple act of carrying a gun would probably only increase my confidence by a few percent.