It's a question that's being asked a lot now, as Woody Johnson, Charley Casserly, and Ron Wolf head to Seattle to interview Dan Quinn, Tom Cable, and others for the head coaching spot. They've said they want to hire a general manager first, and that's the way things are usually, although not always, done. So what gives?
For any coach who is currently in the midst of the playoffs, there's the component of time. Unless their team has a bye this week, as is the case with Quinn and Cable, coaches cannot be interviewed until after they are eliminated from the playoffs or win the Super Bowl. If you wait until everyone is eliminated to start looking at candidates, you could be left with nobody good remaining since the better candidates tend to go quickly.
In addition, starting the vetting process has the additional benefit of making things easier once a general manager has been hired. If the team has already done their preliminary interviews, they can identify the serious candidates and do follow ups with the newly-hired general manager. Woody Johnson has said that he will have a say in the head coach search. If someone is unacceptable to Johnson, for whatever reason, it makes little sense to bring that candidate to the new GM.
Finally, if the search committee finds a star head coach, one that they're confident can lead the New York Jets to the promised land, there's little reason they shouldn't hire them and then find the GM that can execute the HC's vision.
In short, it makes sense because it's early prep work to make the decision easier when it's crunch time.