That high-amp charger likely will not get you any benefit. It is still charging at 5V, just that 2 ports can output up to 2.4A.
The Quick Charge 2.0 chargers, on the other hand, can output 9V or 12V, depending on what the device can handle. This provides more actual watts to the device, while drawing the same charge current.
QC 2.0-compatible devices CAN charge very quickly. The Galaxy Note 4 is one example, apparently.
Unfortunately, with the G4, at the moment using a QC 2.0 charger only provides about a 20% speed increase, max, over a normal high-current charger. Assuming the phone stays cool enough that the the charge current is allowed to stay high. If the phone warms up too much, the charge current will be reduced to about 0.3A, even if you're using a Quick Charge 2.0 charger.
The highest charge current I've seen on my G4, with a QC 2.0 charger, is about 1950mA. And about 1650mA using the LG charger. So I doubt the phone would even make use of 2.4A input.