The short answer is yes, but Edessa was the weakest and most exposed of the Crusader states, and was going to fall some time in the 12th century.
Focusing on the short term, two opportunities were missed. First, the princes of Antioch and Edessa did not cooperate at all with the Byzantines when John II came to the Holy land with large forces in 1138. Eliminating some of the moslem states in the area would have made Edessa more defensible and have given the crusader states more resources when the Zengid attack came.
The second opportunity came during the Second Crusade, when the crusaders didn't try to retake Edessa. They might have failed anyway, given that crusade's dismal outcome across the board in OTL, but if the Germans hadn't been virtually wiped out in Anatolia it might have been possible, especially if the Byzantines could have been brought in as allies.
Finally, the rump state at Turbessel fell after Joscelin II was captured, which was easily avoidable (Joscelin was caught because he stopped to relieve himself), and having a better man than Joscelin in command wouldn't have hurt.