Considering Antioch and Armenia and such served as client states it's certainly not unthinkable for Jerusalem to be reduced to a similar status.
What's Jerusalem and its surroundings like at this stage? Is it worth the trouble for Mongols to garrison it, or would they just want to move on to greener pastures (i.e. Egypt)?
It also depends upon what's happening in Jerusalem at the time- if its being held by a regent for an absent Hohenstaufen or in one of its frequent periods of civil war that'd complicate matters.