Assuming the BMS is correctly designed and working right, it will just turn off all output power once it's current limit is exceeded. So your bike will just shutdown (lose power, turn off) whenever you use the controller's full power.
If the BMS isn't designed or working right, then it won't shut off to protect the cells against overcurrent, and the overload will cause excessive voltage sag (and cell heating and aging), the sag will mean you probably won't actually see any greater power from the higher current above the cells' capabilities, since power (watts) is volts x amps.
As E-HP notes, if you use the KT controller, you can just program it for lower current to match the battery capability, to avoid the problems above altogether.
Note that as the battery ages, it will still sag in voltage more and more at the higher currents. This may cause shutdowns under higher loads as the battery is closer to empty than full once the battery is old enough.
