What would happen if a charger tried to pull more current than a QC 3.0 source can output?
There are four possibilities maybe more but mostly 4.

One the voltage will drop relative to the current being pulled. The voltage source is going out of regulation.

Two the regulator will going into a overload mode and turn off  Many Regulators have self protection circuits. This may cycle on and off until the condition is fixed. 

Three, the circuit will burn or short circuit or some other destructive state. A burned fuse or inductor or mosfet or ic. 

Four, unlikely, the circuit will go into a current limit mode.

There is no way to know without all the part numbers and schematic. Of both your charger and the target (how it will act to under current conditions is even more complicated and guesswork) So best to not overload your circuit. 

The significant difference between the two source power output should be enough to make this common sense.