Some posters also seem to think that everyone will be tracking Joker from the get-go. They won't even know who he is. Joker is flamboyant, but he waits for his moments. As others (and I) have said, it really depends on Joker's mood/motive. If he's causing trouble for stupid reasons like this is a fun vacation for him, then he's tracked and offed as several posters say, I think. But, if he's playing it smart and simply looking to leave this place with a big grin so he can get back to Batsy, the Marvel NYC may be in trouble. He's perfectly capable of biding his time, learning what he can, and setting things in motion on a city-wide level. Honestly, there are many characters in the DCU that are just as capable and willing to take Joker out if prompted to-- Luthor, Deathstroke, Ra's al Ghul, Vandal Savage, etc. who have resources and can see Joker only as useful as bringing chaos to the heroes, but if he gets in their way... yet, they often underestimate the Joker. I'd imagine many Marvel folks might as well. Punchline or Harley or both, Joker has someone who can distract heroes and take the fall when he decimates the city as he tries to head back to Batman. He could even break criminals out to run amok, as he's easily done so in the past.
Now, that's *if* he feels there's a Batman to get back to. If he's trapped in the MU without Batman, who knows what could happen. He's run the gamut of mass-destruction, mourning, going sane, going catatonic, and all points in between when Batman vanishes/dies in various stories. It's too much of a wild card if there's no one he considers a worthy enough foe in MU to challenge and if he truly believes Batman is lost to him forever.