What does voltage output from an SMPS look like when inductor is saturated?
The max current limit on the controller is 2.5A, so the inductor is undersized.  

If you try to draw more than the saturation limit of the inductor, the inductance will decrease and the inductor current will rise rapidly and the part will go into cycle by cycle current limit until the current demand goes below the current limit.  

You could easily overheat the inductor that way, so it would be better to find an inductor that doesn't saturate before 2.5A.

It would certainly cause the output voltage to drop when it happens.