Indeed. And there is going to have to be efforts to convert parts of the local populace as well. The easiest route, of course, is to try to convert the local Christian population, or to bring those Christian churches that exist in the Crusader domain under the umbrella of Rome (as mentioned in my post above). I suspect there will also be a number of formerly Muslim converts who will enter the fold over time - certainly not a huge surge of them, but a steady trickle (likely local elites first, I would think). The latter is especially true the Crusaders don't attach too much of a stigma to the recently converted and if conversion is seen as a way to advance one's career and/or place in society.It seems that while Crusader State has managed to establish itself somewhat, and is certainly in no danger of being swept into the sea by resurgent Muslim nations any time in the near future, is still dependant upon foreign assistance. I mean, from what has been written, they still depend upon Byzantines and occasional "Crusader" forces from Europe for military manpower, since their own manpower pool is still relatively limited, lacking loyal/Christian/Catholic population to be used in both times of peace and war. They need to push for greater immigration of Catholics to the area, to create a better balance to the Muslim and Ortodox population in the area. Although, it will be interesting to see just how economy of the area develops, especially once they conquer Egypt as well, putting them firmly in control of majority of trade Eastwards.
I'm just shooting from the hip, but I suspect that you will see a stratified society emerging for first two generations of so with European crusaders (and their decedents) on top. Then you'd have the converted locals beneath them (obviously augmented by the personal wealth an status of the convert), then steadfast non-Catholic Christians and finally Muslims. Just due to the fact of the population imbalance, I highly doubt you're going to see too brazen of persecutions of the Muslims, and some level of persecution being used to possibly entice local Christians to join the Catholic Church. Over time, of course, the difference between Crusader decedents and converts is going to be minimized due to intermarriage and the like - certainly by the third and fourth generations whatever stigma is attached will likely begin to minimize, though a certain amount of soft snobbery could still be in place.
However, I'm not really taking into consideration the possibility of waves of European emigration, save for Crusaders themselves. The journey is going to be fairly cost prohibitive, I would think, for a peasant to just up and leave for the Holy Land to stake his claim. Those in the nobility, or the lower nobility, might find the move easier and I could certainly see them third or fourth sons making the move. Perhaps the Church offers to help pay for the transportation of immigrants, as well as annulling any feudal obligations peasants have to stay on their Lord's land, if an immigrant cannot pay their own way?
This does, of course, bring up another question, however: how much available land is there in the not-Kingdom of Jerusalem? Its all well and good for immigrants to come there, but if there is no land for them to work, or other ways to sustain themselves, then them showing up on the doorstep might cause more problems in the long run. Laws could be passed, of course, which strip the Muslim population of their land, but that's going to cause a helluva lot of issues.
In any case, the Church is definitely going to be making efforts to convert the locals and, if done right, this could create a base of support for the Crusader state (as well as having some very interesting impacts upon the culture, language and customs that develop in Jerusalem). And if Jerusalem works out a successful program to integrate the locals and create a functioning state, then that can be important (with alterations of course) to Egypt when it eventually falls to the Cross.
P.S. Random thought. I've mentioned the possibility of the local Christian populations (at least some of them) entering into communion with Rome while maintaining their own Rites. However, I wonder if any of them may see it as beneficial to enter into communion with Constantinople instead. After all, the one group that the Crusaders would certainly not persecute are Orthodox Christians who look to Byzantium for protection: at this stage, the Crusaders still need the Empire too much. It would be a good way to snub Rome, while still maintaining some level of autonomy and protection. However, Constantinople remains closer and there is a longer history of distrust there, while Rome itself is far away (though it's representative is far closer). Hmmmmm