Short answer, no. No he shouldn’t.
The long answer is a bit more qualified. It concerns the various roles played by each bowler, and who is in form. Boult and Southee are both new ball bowlers, and Bracewell and Wagner are better coming on at first change. That effectively means that Bracewell would be displacing Wagner, a horribly unfair change given that Wagner has been the best quick bowler for New Zealand so far. While Bracewell’s injury was not as stupidly self inflicted as originally thought, he still opened the door for someone else to take their opportunity. Wagner took the chance with both hands.The other option is that Bracewell comes in for Martin, but that too would be foolish as Martin is in a rich vein of form with both bat and ball. He has been fighting hard for his place and getting results.
There is also the matter of whether Bracewell is an automatic pick any more. Over the past 12 months, his bowling stats are horrendous. In nine test matches he has picked up 18 wickets at 51.94. Those are worse returns that both Chris and Bruce Martin, Neil Wagner, Kane Williamson, even Jeetan Patel. Bracewell burst onto the scene against Australia at the end of 2011, since then he has been frustratingly erratic. He is a young bowler, still developing, and will get more chances. At the moment though he should be working hard to get his spot back.
I would fully expect Bracewell to go on the upcoming tour to England, where he will probably get a game. In the meantime though it would hardly send the right message that he can continue on this trajectory and expect to be picked for the most important match of the summer. The only thing in his favour is that as a fresh bowler he may be brought in due to the short turnarounds between tests. As this is the last of the summer though, it should go to the form players, as a just reward for their hard work over the last few weeks.