I will certainly root for them to win, and at least they don't have anymore Pats, 9'ers, Texans, etc on their schedule. I think it is very extremely unlikely that they'll win out; they've given us no evidence that they're capable of getting on a sustained hot streak this season. But that's why they play the games, any given Sunday, etc, etc. So who knows.
Also, it's hard for me to root for them to lose. I understand that they'll get a better draft pick with a worse record, but do you really want your team to be 4-12 instead of 8-8 or 7-9? You want a sustained, winning, respected franchise. Think Pats or Steelers. They always win and always manage to do just fine with their drafts to replenish talent.
Now of course I'm not saying I think the Jets will be the Pats or Steelers overnight, but I guess I'm just stating what I think is the obvious - that's the winning culture you want to strive to build over time. So cheering for one's team to lose games for a better draft pick or to nudge the owner to blow things up seems counter intuitive to me.