It would help in certain circumstances and hurt in others. Theoretically, having one state means it would be easier to summon the resources of the entire Outremer in a unified chain of command. In practice, the Kingdom of Jersualem is not a centralized state and the king always had to deal with unruly vassals. We've just made Antioch and Tripoli the most powerful of the unruly vassals instead of independent rivals/allies. A disadvantage is that once one state is pulled into war, they are all. No one is able to negotiate separately to avoid being sucked in.
The only way I see this making the situation better is if the circumstances allow the Kingdom of Jerusalem to significant expand in the time period most favorable to it - between the founding of the state and before the rise of Saladin. If it allows the Kingdom to seize Aleppo or even Damascus, then it would significantly reduce the strategic risk to the kingdom. If not, then having one state probably won't improve its chances for survival.
The problem is now that the Antiochene vassals will hate paying tribute to the king of Jerusalem, not to mention that those Normans were unruly characters to the last degree. Jerusalem might be a more distracted kingdom internally, having to put down the Antiochene vassals, because they will try to test the authority of Jerusalem. The second problem is that Edessa is going to be hard to defend, if Jerusalem is the capital. It was hard to defend, when Antioch and Edessa were aligned and Edessa was an independent kingdom, with the king on the spot. Edessa, ITTL, will fall faster (the temptation to fall behind the Euphrates will be high). And Antioch will lose its outer gate.
Of course, some of this can be overcome if the Normans are made kings of Jerusalem (but this might upset the Franks, who, having no reason to stay, will simply return home after the first Crusade, leaving fewer soldiers to guard the Kingdom.
Of course, having the Byzantines keep Antioch is a departure in its own right. If I remember right, that was supposed to have been the price of Byzantine support for the First Crusade. If Constantinople gets Antioch, then Byzantium and Outremer might have better relations and cooperate better against their common enemy.
What are you going to do with the Normans? They were at odds with the Byzantines, and they are simply not going to bow to the Emperor (or anyone else, for that matter).