No; the Mamluks only fought a true Mongol army once, and on that occasion -- the overblown victory at A'in Jalut -- only half of the army was actually Mongol, the rest being composed of the same Christian allies who sacked Baghdad while the Mongols watched. The bulk of Hulegu's army was already withdrawing towards Iran.

On all other occasions, they fought the Ilkhans and their forces, which were Turkic and Iranian, like every force from Iran since the Seljuks. Ethnic Mongols were outnumbered by at least 1000 to 1 in Iran, anthropologists estimate.