Yes. At the end of the novel, an atomic bomb is dropped and completely destroys the city. After the city is destroyed, the traveling intellectuals sit around a fire to eat a meal. Granger begins to speak about a mythical bird called a Phoenix. He mentions that every few hundred years the bird would build a funeral pyre and burn itself up. The Phoenix would then spring from the ashes and be born all over again. Granger believes humanity is essentially doing the same thing by destroying itself and starting over again. He goes on to say,
And it looks like we're doing the same thing, over and over, but we've got one damn thing the Phoenix never had. We know the damn silly thing we just did. We know all the damn silly things we've done for a thousand years and as long as we know that and always have it around where we can see it, some day we'll stop making the goddamn funeral pyres and jumping in the middle of them (Bradbury 156).
Granger's comparison is accurate and adds to the significant theme of the novel, which is that books are important to remind humanity of our past mistakes. Through the characters of Faber and Granger, Bradbury argues books preserve knowledge and prevent us from repeating our past failures. Similar to how the Phoenix continually destroys itself, humanity is also destructive. Bradbury's predominant message and theme is that books are essential to end humanity's cycle of destruction by learning from our past mistakes.
I think that you can argue that it does. I think that one of the major themes in the novel is the idea that a society like the one Montag is living in must be destroyed pretty completely before a new one can be made.
We see this in some of the things that Faber says to Montag. He tells him that the goal should be simply to hold on until something happens and they can start the society again. Maybe if that happens they will do a better job the next time.
So we have this idea that the society needs to burn like the phoenix so it can rise again from the ashes.