Georgia very indirectly, mainly by keeping restless Turks busy up in the north. But the Christian/Islam border areas are pretty small and its no big deal for Turks from the north to head to Syria to fight in the hope of plunder.
Yeah. Still, its not as useful as say, Byzantium or Armenia, which are in the theater directly.
Of course, a strong Byzantine state will have its own interest in the fate of the Crusader States, namely making them vassals if not fully incorporated into the empire, as mentioned by BG.