It is definitely possible to argue this issue from both angles. Firstly, as Montag himself realises, it is possible to say that Beatty wanted to die. The way he is able to quote from so many books and yet spends his life burning them and attempting to destroy them points towards some deep inner inconsistency that, it could be argued, meant that he as a character experienced massive internal conflict. This is something that Montag realises after he has killed Beatty, and reflects on his character and how he acted in his last few moments:
He had just stood there, not really trying to save himself, just stood there, joking, needling, thought Montag, and the thought was enough to stifle his sobbing and let him pause for air.
Such a realisation is based on the way in which Beatty was a character torn in two by internal conflict, and how in Montag he was able to find an escape from that conflict. Beatty wanted to die, it is possible to argue, through the way in which he actively sought out an opportunity to get himself killed and then dared Montag to do it in a very challenging way.
However, at the same time, there is enough evidence in the text to suggest that Beatty definitely did not want to die, and that he never thought Montag would go through with it and kill him. Note, for example, the way in which Beatty's eyes "widened the faintest bit" when he saw Montag's fingers twitch the safety catch on the flame thrower. This, combined with the way in which Beatty has always been successful before in facing down Montag in discussion, could lead the reader to believe that there was no way in which Beatty actually wanted to die: he had every belief that Montag would back down when challenged openly like he had backed down before whilst in the fire station. Even when Montag thinks that Beatty wanted to die, he concludes that it is "strange," suggesting perhaps that Montag's revelation is more to do with assuaging his own guilt than anything else.