It is perhaps fitting that Montag defies Beatty and attempts his escape when war breaks out. He leaves a society which was intellectually dead and then poised to destroy another and/or be destroyed itself. There is "a time for war, and a time for peace." This might hint at a peaceful time following the war. Ecclesiastes also warns about vanity; and this also applies to Montag's old society. They believed they had the answers in structuring a society based upon limiting knowledge.
The choice of Ecclesiastes is also ironic because this book warns about too much knowledge. "For in much wisdom is much grief: and he that increaseth knowledge increaseth sorrow." Ecclesiastes also seems to offer contradictory maxims so it is difficult to say how this applies to Montag. Given these contradictions (wisdom is useless and/or wisdom is better than folly), we could say that the reader is given a choice. In this way, it is applicable to Montag because he is fleeing a society in which he had no choices. His affirmation of literature and knowledge is predicated on his ability to choose knowledge, books, etc.
The notion that there is a time for everything is useful in considering how - as Montag changes, so might the world. However, this notion is also in the context of things being preordained; and this goes against the notion of Montag using his intellect to "choose" a new path for himself. This is the contradiction if we consider that Montag's new life is based upon his own free will. On the other hand, the idea that everything is preordained (has been written) works well with the novel because a rediscovery of ancient literature helps to foretell how things can change.