The historical reaction of Russians has *always* been to centralize power in the face of a threat. In fact, they tend to gravitate toward centralizing power even when there *isn't* any threat.
But, that said, the question here is whether Putin has got some real reason for grabbing power in order to combat terrorism, or whether he's just grabbing power because he's a megalomaniac, and using the latest terrorist atrocity as an excuse.
It's easy, and obvious, to jump to the latter conclusion - but the fact remains that terrorists are able to operate freely inside Russia, bribe their way onto Russian airliners, get the cooperation of law enforcement, etc. etc. Imagine if you had the Chief of Police of some medium-sized city in Massachusetts cooperating with al-Quaida, and you'd have something analogous to what's going on inside Russia. Putin may think - rightly or wrongly - that the only way he can stop that sort of shenanigans is by obtaining dictatorial powers.
You are more than correct. If they don't get the bribe problem under control then nothing they do is worth anything.