No, because the mongols would still come and burn Baghdad, the center of Islamic learning, to the ground.The Crusades were without a doubt some of the most pivotal times in Western civilization. The Muslim world was flourishing technologically, medically, culturally, academically, and had a relatively peaceful existence within the borders of the Islamic realm. Christendom was bitterly divided. Kingdom against Kingdom and God was on both sides. The nobility horded all of the wealth and comfort while the serfs and peasantry begged for scraps.
Christedom was experiencing the Dark Ages, and Islam was reaching its pinnacle. But the Crusades changed all of that. Well-armored Christian armies had little difficulty defeating unarmored Arabs in the First Crusade. And the Christians would stay in the Holy Land for another 300 years.
The Crusades left the Islamic world in disarray and turmoil. Perhaps hundreds of thousands of Muslims died and their civilization had almost fallen. Christendom put Islam in the Arab Dark Ages.
What would have happened if the Pope had never called for a Crusade? What if the Muslim world continued to rise in its power? What if they eventually had the ability to march into Europe and conquer Rome? Could the Muslims have defeated the Christians on their own soil?