Surviving Khwarezmian Empire Impact on Crusader States?

Surviving Khwarezmian Empire Impact on Crusader States?

The fall of the Khwarezmian Empire to the Mongols had a significant impact on the Crusader states. Many Khwarezmian warriors fleeing the destruction of their homeland served as mercenaries for the Ayyubid Sultanate. The Khwarezmians in 1244 sacked Jerusalem and helped destroy a Crusader army at La Forbie.

What would have happened had the Khwarezmian Empire defeated the Mongols? Based on my poll in another thread and information I've read they seemed in a good position. They had the advantages in terrain, a massive standing army and actually managed to defeat the Mongols in one battle
 
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